c and d please! This exercise demonstrates that, in general, the results providedby Tchebysheff's theorem cannot be improved upon. Let Ybe arandom variable such thatp(-1) = –, p (0) = º, p(1) ==18 P(1) =18a Show that E(Y) = 0 and V(Y) = 1/9.b Use the probability distribution of Yto calculate P (|Y – el2 30).Compare this exact probability with the upper bound provided byTchebysheff's theorem to see that the bound provided byTchebysheff's theorem is actually attained when k 3.*c In part (b) we guaranteed E(Y) = 0 by placing all probabilitymass on the values -1, 0, and 1, with p(-1) = p(1). The variance wascontrolled by the probabilities assigned to p(-1) and p(1). Usingthis same basic idea, construct a probability distribution for arandom variable X that will yield P (X- ux| 2ox) = 1/4.*d If any k> 1 is specified, how can a random variable Wbeconstructed so that P (W - wl2 kow) = 1/k-?

Name: c and d please! This exercise demonstrates that, in general, the resul
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: c and d please! This exercise demonstrates that, in general, the results providedby Tchebysheff's theorem cannot be improved upon. Let Ybe arandom variable such thatp(-1) = –, p (0) = º, p(1) ==18 P(1) =18a Show that E(Y) = 0 and V(Y) = 1/9.b Use the