The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.
LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.
Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.
The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.
In mathematical terms, the OLS method can be represented as follows:
minimize the sum of squared vertical differences,
min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²
However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.
In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
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Which set of steps shows how to find f(-3) when f(c)=-4x-5?
Answer:
7
Step-by-step explanation:
f(-3)
f(x) = -4x-5
f(-3) = -4(-3) - 5
f(-3) = 12 - 5
f(-3) = 7
the weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. what is the probability that the next report will weigh less than 45g?
The probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%. We can use the standard normal distribution to find the probability that the next report will weigh less than 45g.
z = (x - mu) / sigma
where z is the standard score, x is the value we want to standardize (45g), mu is the mean (60g), and sigma is the standard deviation (12g).
Substituting the given values, we get:
z = (45 - 60) / 12
z = -1.25
Next, we use a standard normal distribution table (or a calculator) to find the cumulative probability of z being less than -1.25. This gives us:
P(z < -1.25) = 0.1056
Therefore, the probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%.
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how many uniforms can you make
Answer:
39
Step-by-step explanation:
165 and 3/4 is equal to 165.75 and 4 and 1/4 is 4.25
165.75/4.25=39
39 uniforms could be made
Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 642 total miles?
The equation to represent the given scenario is 642=239+64x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour.
Let x be the number of hours.
We know that, Distance =Speed×Time
Now, total distance = 239+64×x
642=239+64x
Therefore, the equation to represent the given scenario is 642=239+64x.
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A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the
accompanying table. Write the linear regression equation that represents this
set of data, rounding all coefficients to the nearest tenth. Using this equation,
estimate the homework grade, to the nearest integer, for a student with a test
grade of 31.
Homework Grade (x) Test Grade (y)
The regression equation is y = x - 10.4
Homework grade (x) = 41
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
From the table,
We have ∑X = 488, ∑Y =439, ∑XY = 31458, ∑X² = 34834, n=7
Standard linear equation is y= a+bx
a= [ ∑Y × ∑X² - ∑X × ∑XY ]/ [ n × ∑X² - ( ∑X)² ]
On substituting and simplifying , we get a= -10.4
b= [ n × ∑XY - ∑X × ∑Y ] / [ n × ∑X² - ( ∑X)² ]
On substituting and simplifying , we get b ≈ 1
The regression equation is y = x - 10.4
Given test grade y=31
We have 31=x-10.4 => x= 41.4
Nearest integer is 41
Homework grade (x) = 41
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a box contains 12 balls of which some are red in colour. if 6 more red balls are put in the box and a ball is drawn at random the probability of drawing a red ball doubles than what it was before. find the number of red balls in the bag.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added.
Let's assume that there are initially "x" red balls in the box. This means that there are (12 - x) non-red balls in the box.
When 6 more red balls are added, the total number of red balls becomes (x + 6), and the total number of balls in the box becomes (12 + 6) = 18.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added. This means that the probability of drawing a red ball before the extra balls were added was:
P(red) = x / 12
And the probability of drawing a red ball after the extra balls were added is:
P(red) = (x + 6) / 18
We are also told that the second probability is twice the first:
(x + 6) / 18 = 2 * (x / 12)
Simplifying this equation, we get:
(x + 6) / 9 = x / 6
Multiplying both sides by 18, we get:
2(x + 6) = 3x
Expanding the left-hand side, we get:
2x + 12 = 3x
Subtracting 2x from both sides, we get:
12 = x
Therefore, there are initially 12 red balls in the box.
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magic the gathering is a popular card game. cards can be land cards, or other cards. we consider a game with two players. each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand. (a) assume that player one has 10 land cards in their deck and player two has 20. with what probability will each player have four lands in their hand? (b) assume that player one has 10 land cards in their deck and player two has 20.with what probability will player one have two lands and player two have three lands in hand? (c) assume that player one has 10 land cards in their deck and player two has 20. with what probability will player two have more lands in hand than player one?
Probability the player two have more lands in hand than player one is:
A) 0.0135
B) 0.102
What is probability?
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
Here, we have
Given: each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand.
A ) probability of each player having four lands in their hand
Given data:
player 1 has 10 land cards
player two(2) having 20 land cards
Hence, the probability can be calculated as
= 0.0135
B) probability of player one having two lands and player two having three lands in hand
Given data:
player one (1) has 10 land cards
player two has 20
Hence, the probability of player one having two lands and player two having three lands in hand can be calculated as attached below
= 0.102
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a force of 192 lb is required to hold a spring stretched 3 ft beyond its natural length. how much work w is done in stretching it from its natural length to 9 inches beyond its natural length?
The work required to stretch the spring from its natural length to a distance of 9 inches beyond its natural length is 2.25 lb-ft.
The problem involves calculating the work required to stretch a spring from its natural length to a distance of 9 inches beyond its natural length, given that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length.
To solve the problem, we use the formula for the work done by a force that varies with distance, which is given by:
W = (1/2) k (x2^2 - x1^2)
where W is the work done, k is the spring constant, x1 is the initial distance, and x2 is the final distance.
In this case, the initial distance is the natural length of the spring, which is 0 ft, and the final distance is 9/12 ft. To find the spring constant, we use the fact that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length, which gives us:
192 = k * 3
Solving for k, we get k = 64 lb/ft.
Substituting the values into the formula, we get:
W = (1/2) * 64 * (9/12)^2
Simplifying, we get:
W = 2.25 lb-ft
This calculation shows how the work done by a force that varies with distance can be calculated using the spring constant and the distances involved.
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Which is larger? Circle A with an area of 10562.96 cm squared, or circle B with a circumference of 357.96 cm?
Circle A is larger.
Circle A's radius is 58 cm and circle B's radius is 57 cm.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Area of a circle = πr²
Circumference of a circle = 2πr
Circle A:
Area of a circle = 10562.96
πr² = 10562.96
r² = 3364
r = 58 cm ____(1)
Circle B:
Circumference = 357.96
2πr = 357.96
r = 357.96/6.28
r = 57 cm ______(2)
From (1) and (2)
58 > 57
So,
Circle A is larger.
Thus,
Circle A is larger.
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What is the HCF of 1854 and 81
The highest common factor, HCF of 18, 54, and 81 is 9.
What is the highest common factor?The highest common factor is the highest factor or number that can divide two or more numbers evenly without a remainder.
The common factors of 18, 54, and 81 are 1, 2, 3, 6, and 9 because each of these numbers can divide the three numbers without a remainder.
Based on the common factors of 18, 54, and 81, we can identify that the highest factor is 9.
The highest common factor, HCF, is also described as the greatest common factor, GCF.
Thus, the HCF of 18, 54, and 81 is 9.
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Complete Question:What is the HCF of 18, 54, and 81?
a publishing industry report predicts that magazine subscriptions will drop by 10% each year if this prediction is correct then how many subscribers will a magazine with 98000 subscribers have in 10 years (round to the nearest whole number if necessary)
Rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.
What is whole number?
A whole number is a positive integer that doesn't include any fractional or decimal component. Whole numbers include positive integers such as 0, 1, 2, 3, 4, and so on. Whole numbers do not include fractional numbers or decimals, such as 0.5, 1.7, and so on. Whole numbers are used to count items or represent discrete quantities, such as the number of people in a room or the number of apples in a basket.
If the prediction that magazine subscriptions will drop by 10% each year is correct, then in 10 years the number of subscribers for a magazine with 98000 subscribers will be:
98000 * (1 - 0.10)^10 = 98000 * 0.3548 = 34638 subscribers
So, rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.
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Subtract. Write the answer in standard form.
(13 + 9i) - (1-11) ?
Answer:
[tex]10^{1}[/tex]
Step-by-step explanation:
13 + 9 - 1 - 11
Add 13 and 9 to get 22.
22 - 1 - 11
Subtract 1 from 22 to get 21.
21 - 11
Subtract 11 from 21 to get 10.
10
HELPP please
Find the length of the unknown side of the triangle.
10 ft
5 ft
The length of the unknown side of the triangle is
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answer: [tex]5\sqrt{5} \ \text{ feet}[/tex]
Work Shown:
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+10^2}\\\\c = \sqrt{125}\\\\c = \sqrt{25*5}\\\\c = \sqrt{25}*\sqrt{5}\\\\c = 5\sqrt{5}\\\\[/tex]
For more information, search out "pythagorean theorem".
a certain country's factory sales of electronic goods to dealers from 1990 through 2001 can be modeled as
The factory sales of electronic goods from a certain country to dealers from 1990 to 2001 can be modeled using a mathematical equation .
Modeling factory sales of electronic goods from a certain country to dealers from 1990 to 2001 involves creating a mathematical equation to represent the data . To begin, one must collect the data from the sales of electronic goods from the given country to dealers from 1990 to 2001. This data should include the total amount sold for each year. Once the data is collected it must be organized into a visual representation, such as a line graph or a scatter plot. The visual representation should then be examined for patterns in the data which can be used to create a mathematical equation. This equation should be able to accurately describe the data and be able to predict future data points. The equation should then be tested to ensure accuracy before it is used to model the factory sales data.
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Combine like terms to simplify the expression:
1. 17
−
0. 07
�
+
(
−
3. 92
�
)
1. 17−0. 07a+(−3. 92a)
So the simplified expression of the expression given in the question is: 1.17 - 3.99a
To simplify the expression, we can combine the like terms, which are terms with the same variable and exponent. Starting with the first two terms: 1.17 - 0.07a. The next two terms are the opposite of each other, so we can add them: 1.17 - 0.07a + (-3.92a) = 1.17 - 0.07a - 3.92a. Finally, we can simplify the expression by combining the like terms, which are terms with the same variable: 1.17 - 0.07a - 3.92a = 1.17 - (0.07 + 3.92)a = 1.17 - 3.99a. So the simplified expression is: 1.17 - 3.99a
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Complete Question
Combine like terms to simplify the expression:
1. 17 − 0. 07 + ( − 3. 92 ) 1. 17−0. 07a+(−3. 92a)
c) In the following figure, AE = 8 cm, BE =3 cm and CE = 4 cm. Find the length of DE .
Answer:
DE = 6 cm
Step-by-step explanation:
The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:
CE × DE = AE × BE
4 × DE = 8 × 3
4 × DE = 24
DE = 6 cm
Hope this helps!
dave wants to buy a new collar for each of his 5 cats. the collars come in a choice of 9 different colors. step 1 of 2 : how many selections of collars for the 5 cats are possible if repetitions of colors are allowed?
If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:
9 x 9 x 9 x 9 x 9 = 59,049
In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:
Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
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Write an equation in point-slope form for the given point and slope:
Point: (4, -6)
Slope: 2
Answer:
y = 2x -14
Step-by-step explanation:
The point-slope form is y = mx + b
m = 2
y-intercept is located at (0, -14)
So, the equation is
y = 2x - 14
Answer:
y-6=2(x-4)
Step-by-step explanation:
point-slope form y-y1=m(x-x1)
every time these two wheels are spun, two numbers are selected by the pointers. what is the probability that the sum of the two selected numbers is even?
The probability that the sum of the two selected numbers is even is 1/2.
The parity of the two chosen numbers must match for the sum to be even.
Given this information, we can divide the larger problem into smaller ones. First, we may determine the likelihood that the first spinner will land on an even number.
Exists a [tex]$\frac{1}{2}$[/tex] chance that this happens, and a [tex]$\frac{1}{3}[/tex] there is a chance that the second spinner will also land on an even number, hence
[tex]$\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$[/tex]
There is a win if both the first and second spinners land on an odd number.
[tex]$\frac{1}{2} \cdot \frac{2}{3} = \frac{2}{6}$[/tex]
chance of this happening. Adding these two probabilities together, we get
[tex]\frac{1}{6} +\frac{2}{6} =\frac{3}{6} =\frac{1}{2}[/tex]
Therefore, The probability that the sum of the two selected numbers is even is 1/2.
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There are total of 452 cows and goats in a farm. 5/7 of
the cows are equal to 13/27 of the goats in the farm.
Find the total number of legs of cows.
The total number of cows is given by the equation c = 182 cows and the total number of legs of cows is n = 728 legs
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The total number of cows and goats = 452
So , c + g = 452 be equation (1)
And , ( 5/7 )c = ( 13/27 )g
On simplifying the equation , we get
c = ( 13 x 7 ) / ( 5 x 27 ) g
c = ( 91/135 )g be equation (2)
Substituting the value of c in equation (1) , we get
( 91 / 135 ) g + g = 452
On further simplification , we get
( 91 + 135 ) / 135 g = 452
( 226 / 135 ) g = 452
Divide by 226 on both sides of the equation , we get
( 1/135 )g = 2
Multiply by 135 on both sides of the equation , we get
g = 270 goats
Now , the number of cows = 452 - 270 = 182 cows
The number of legs = 182 x 4 = 728 legs
Hence , the number of cows is 182 cows
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What is the area of the figure?
(NEED THE ANSWER ASAP. PLEASE DONT PUT ANYTHING NONSENSE OR I'LL REPORT U. THANK U FOR UR HELP)
The area of the given figure is 12 square meters
The given figure is a parallelogram
Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four
The height of the parallelogram = 2 meters
The base length of the parallelogram = 6 meters
The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram
Substitute the values in the equation
The area of the parallelogram = 2 × 6
Multiply the numbers
= 12 square meters
Therefore, the area is 12 square meters
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I have solved the question in general , as the given question is incomplete
The complete question is :
What is the area of the figure ?
the measure of one interior angle of a parallelogram is 0.25 times the measure of another angle.
The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.
A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:
Angle 2 = (Angle 1) / 0.25
For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.
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Can someone help me with this question i dont get it
Answer:
Step-by-step explanation:
The equation connects m and n.
Suppose n=1,
m=3/1=3.
If n=2,
m=3/2=1.5
If n=3,
m=3/3=1. This shows that as n increases, m decreases.
If m was equal to 1,
1=3/n
Thus n=3.
If m=2,
2=3/n
n=1.5
If m=3,
3=3/n
n=1.
This also shows that as m increases, n decreases.
Hope this helps :)
Answer:
When I increased n, m decreased.
When I increase m, n decreases
Step-by-step explanation:
Let's say that m is one and n is 3
1 = [tex]\frac{3}{3}[/tex] Us this as our base to compare increasing m and n.
Increase n to 6
[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]
When I increased n, m decreased.
Increase m to 3
3 = [tex]\frac{3}{1}[/tex]
When I increase m, n decreases
Amy ray Kim and jammel are on a Trivia team. They gained for correct answers and lose points for incorrect answers. During the contest, Amy gains 3 point, ray loses 4 point, Kim loses 2 points, and jammel gains 5 points. How many points does a team have at the end of the contest?
Answer:
2
Step-by-step explanation:
Amy +3
Ray -4
Kim -2
Jammel +5
So,
3 - 4 - 2 +5 = ?
Answer is 2 points.
Identify the range of the function shown in the graph.
Range of the function shown by the graph is (-∞ , ∞)
What is range?Range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest.
The range is the set of possible output values, which are shown on the
y -axis.
Given,
Graph of a function,
Range represents the y-coordinate of the function.
By the graph,
Range of the function is -∞ < y < ∞.
In interval notation,
Range = (-∞ , ∞)
Hence, (-∞ , ∞) is the range of the function shown by the graph.
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word problem using division where the answer is 64
Answer:
Step-by-step explanation:
There are 256 people in a room. If they are divided into groups of 4, how many groups are there?
Answer: 64
8. A In rectangle ABCD, AC and BD are diagonals. If m/1 = 55, find ABD.
The value of m∠ABD is equals to 125 degrees.
What is a rectangle ?
Rectangle can be defined in which opposite sides are equal.
AC and BD are diagonals of the rectangle ABCD.
Angle ABD is adjacent to angle 1 and angle ABO, where O is the intersection of diagonals AC and BD.
We know that m∠1 = 55, and we can find m∠ABO using the fact that the diagonals of a rectangle bisect each other. Since angle AOB is opposite to side AB, which is congruent to side CD, we have:
m∠ABO = 180 - m∠AOB
= 180 - (180 - m∠1) / 2
= 180 - (180 - 55) / 2
= 62.5
Therefore, we can find m∠ABD by adding m∠ABO and m∠DBO, where DBO is congruent to ABO:
m∠ABD = m∠ABO + m∠DBO
= m∠ABO + m∠ABO
= 2m∠ABO
= 2(62.5)
= 125
Hence, The value of m∠ABD is 125 degrees.
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A pole leans away from the sun at an angle of 7°
to the vertical, as shown in Figure 27. When the
elevation of the sun is 55°, the pole casts a shadow
42 feet long on the level ground. How long is the
pole? Round the answer to the nearest tenth.
Using trigonometric ratio, the height of the pole is approximately 60 feet
What is angle of elevationThe angle of elevation is the angle between the horizontal and a line from the observer to a point above the horizontal. In other words, it is the angle between the ground and the line of sight to an object above the ground.
Using trigonometric ratio to solve the angle of elevation problem, the height of the pole can be calculated using the tangent of the triangle.
tanθ = opposite / adjacent
tan 55 = x / 42
x = 42 * tan 55
x = 59.98 ft≅ 60 feet
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An equilateral triangle with side length 3 cm is shown in the diagram, work out the height of the triangle.
Give your answer rounded to 1 DP.
Answer:
The height of an equilateral triangle can be found using the Pythagorean theorem by treating it as a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. In this case, the side length of 3 cm is the shorter leg, so the height (the longer leg) is 3√3 cm. Rounding to 1 decimal place, the height is approximately 5.1 cm.
the probability that a product will operate properly within an expected time frame is the dimension of quality known as
The probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability
The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one
Here, the product will operate properly within an expected time frame is the dimension of quality
Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability
Therefore, the given statement is know as the reliability
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