a) To find the value of a, we need to integrate the PDF from 0 to 1 and set it equal to 1 since a is a normalizing constant:
∫01 aθ(1−θ)2dθ = 1
Using the formula given, we can simplify the integral:
a ∫01 θ1(1−θ)2dθ = 1
a (1!) (2!) / (1+2+1)! = 1
a (2/6) = 1
a = 3
Therefore, the value of a is 3.
b) To find E[Θ2], we need to use the formula for the expected value:
E[Θ2] = ∫01 θ2fΘ(θ)dθ
Substituting the given PDF and the value of a, we get:
E[Θ2] = ∫01 θ2(3θ(1−θ)2)dθ
Simplifying the integral using the formula given, we get:
E[Θ2] = 3 ∫01 θ3(1−θ)2dθ / 4
E[Θ2] = 3 (3!) (2!) / (3+2+1)! / 4
E[Θ2] = 3/20
Therefore, E[Θ2] is equal to 3/20.
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taper shears, also known as thinning shears, are used on the ends of the hair to create: A) mobility B) Precise lines
C) A clean blunt edge
D) broom like affect
Taper shears, also known as thinning shears, are used on the ends of the hair to create A) mobility.
What are taper shears?Taper shears are designed to remove bulk from the hair without creating a blunt edge, which allows the hair to move more freely and naturally. This can be particularly useful for creating textured or layered hairstyles, where a more uniform look is not desired.
Thinning shears can also be used to blend different sections of the hair together, creating a seamless transition between layers or sections. While taper shears can be used to create some degree of precision, their primary purpose is to add movement and texture to the hair. They are not typically used to create a clean, blunt edge or a broom-like effect.
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a frame which holds the color filter in the guides at the front of a lighting instrument. usually constructed from metal or flame-resistant cardboard.
A frame that holds the color filter in the guides at the front of a lighting instrument is called a "gel frame" or "color frame."
It is usually constructed from metal or flame-resistant cardboard to ensure durability and safety during usage. The frame helps in achieving the desired color effects in various lighting applications.The frame which holds the color filter in the guides at the front of a lighting instrument is commonly referred to as a "gel frame."Gel frames are typically made of metal or flame-resistant cardboard, and they are used to hold color filters (or gels) in place in front of a lighting instrument's lens. The gel frame is inserted into the guides at the front of the lighting instrument, and the color filter is then inserted into the frame.
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