Course Solutions Uncategorized (Solved) : 2 20 Pts 10 Pts Let X Random Variable Taking Values 0 Zi Z2 Z3 1 Probabilities P 1 4 P2 1 Q32707420 . . . .

(Solved) : 2 20 Pts 10 Pts Let X Random Variable Taking Values 0 Zi Z2 Z3 1 Probabilities P 1 4 P2 1 Q32707420 . . . .

 

2. (20 pts) (a) (10 pts) Let X be a random variable taking the values 0 < ZI < z2 < z3 < 1 with probabilities p 1/4,p2-1/2,ps-1/4, respectively. Let the cumulative distribution function of X be P[X = F(x). Define U = F(X). Find and plot (carefully!) the distribution function for U, that is, G(u) PU(X) . (b) (10 pts) Let X be a random variable taking the values _ < < < xn < 00 with probabilities pi1 such that pi >0 and P. Let F be the cumulative distribution function of X and define l-F(X). As in part (a), Let G(u) = PU(X) function. Show that the corners of the steps lie on a line, and find a formula for this line.

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