Consider the discrete random variable x with probability distribution p(x). Denote the mean and standard deviation of x as μ and ox, respectively. Now define a new discrete random variable y defined as y = μx - 3x. (a) What is the mean of y, y, in terms of u? (b) What is the standard deviation of y, oy, in terms of ox? (c) Now consider a new random variable z = μx ax, what value of a is the mean of z, z, equal to zero? where a is some constant. For

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Q: (a) A lower bound for P(6<Y <24) (b) the value of k such that P(|Y-15| ≥k) ≤ 0.09.

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A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

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Q: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2…

A: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2 +…

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