2) Consider the random variable Y has a normal distribution with the following probability density function 1 -y²+44y-484 18 f(y) 3/27 0 < Y a) What is the mean and variance of Y? ɔ) What is the median of Y?

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A: Given,f(x)=x0&lt;x&lt;12-x1≤x&lt;20elsewhere

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A: Given, X~ Gammaα=4,β=4 Y=X2

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A: From the given information, fy=24y10+2y-0.3y210000, 0&lt;y&lt;10 Consider, Ey=∫010yfydy…

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A:

Q: Consider two continuous random variables X and Y characterized by the following joint probability…

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Q: Suppose that the random variable X has the probability density function ( c(1- x²) f(x) = for -1 < x…

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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X² – 10X +…

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Q: 2. If a random variable X has a uniform density with the parameters a=4 and B = 5, find its Density…

A: A random variable X has a uniform density with the parameters α=4 and β=5

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A: The provided joint probability mass function is:

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A: f(x,y)=ye-y(1+x)        x,y&gt;0

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A: To plot p.d.f. of x, we represent X on X axis and value of probability at X on Y axis.

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Q: and arsenide is independent of producing a high percentage of workablewafers, which are the main…

A: It is an important part of statistics. It is widely used.

Q: 1. Let X be a random variable with probability density function f(x) = {k(4 – x²) -2<x<2 otherwise…

A: #1     X   be a random variable with pdf                      f(x)  = k(4-x2)      -2 &lt; x &lt; 20…

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Q: 5. If the probability density function of a continuous random variable X is (cz" 0<x<1 f(r) =…

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Q: Suppose that the joint density function of the random variables X and Y is      f(x,y)=k(1+2y), if…

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Q: 4. Suppose that the joint distribution of X and Y can be modeled by the following probability…

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A: To find k k∫02(x3+x) =1kx44+x2202 =1k164+42 =1k=16

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A: From the given information, fXx=1aux-ux-10fYy=1bux+10-ux-10 The above density can be written as,…

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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…

A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25