2. Consider the random variable Wn with P[W₂ = 0] = 1 and P(Wn an) for some constantsan, n = 1, 2, ... 9 n n (a) For eac

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2 Consider The Random Variable Wn With P W 0 1 And P Wn An For Some Constantsan N 1 2 9 N N A For Eac 1 (68.51 KiB) Viewed 38 times

2. Consider the random variable Wn with P[W₂ = 0] = 1 and P(Wn an) for some constantsan, n = 1, 2, ... 9 n n (a) For each given sequence an, find the limits as n → ∞, when existing, for Wn, E[Wn], and Var[W]. (i) an = 1/n. (ii) an = 1. (iii) an √n (iv) an = n. (v) an = n². = (b) For which sequences an in part (a) can one use Chebyshev's inequality to find the limit of Wn in probability? (c) Does Wn →p c imply that E[W₁] → c? =