Class problem set 1 - X E(Y)=μ Y Var(X)=σ 2 x Var(Y)=σ 2...

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Class problem 1 Consider the following probability distribution for random variable X. X f x or P(X=x) 0 0.10 1 0.20 2 0.40 4 0.15 7 0.10 8 0.05 Find: (you need to show your work) a. Mean=μ=E(X) b. E(3X) c. Is E(3X)=3E(X)? d. Var(X)=σ 2 e. Var(X+2) f. Var(3X) g. Is Var(3x)=3Var(X)? h. Standard Deviation Std(X)=σ i. Is Std(3X)=3Std(X)? Class Problem 2 Use the following bivariate table for random variables X and Y to answer the questions. X 1 2 5 2 0.05 0.15 0.10 Y 3 0.10 0.20 0.05 4 0.15 0.20 0.00 a. Find unconditional mean and variance of X and Y; E(X)=μ
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