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4.4.19 Random variableX has PDE fx(a)-1/4 -1s-33, 0 otherwise Define the random variable Y by Y = h(X)X2. (a) Find E[X and VarX (b) Find h(E[X]) and Eh(X) (c) Find ElY and Var[Y .4.6 The cumulative distribution func- tion of random variable V is 0 Fv(v)v5)/144-5<7, v> 7. (a) What are EV) and Var(V)? (b) What is EIV? 4.5.4 Y is an exponential random variable with variance Var(Y) 25. (a) What is the PDF of Y? (b) What is EY ]? (c) What is PIY > 51? .5.13The probability density function of random variable X is otherwise (a) What is Pl X 2)? (b) What is Fx(z), the cumulative distri- bution function of X? (c) What is E X], the expected value of X? (d) What is Var[X], the variance of X?
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