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Class problem 1 Consider the following probability distribution for random variable X. X fxor P(X=x) 00.10 10.20 20.4040.1570.1080.05Find: (you need to show your work) a.Mean=μ=E(X)b.E(3X)c.Is E(3X)=3E(X)?d.Var(X)=σ2e.Var(X+2)f.Var(3X)g.Is Var(3x)=3Var(X)?h.Standard Deviation Std(X)=σi.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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