Asked Aug 20, 2019

Let Z1,...,Zn be a sequence of random variables. For every n = 1, 2;..., P(Zn =
n^2) = 1/n, and P(Zn = 0) = 1 - 1/n. In other words, Zn is binary. Show that
(a) limit as n goes to infinity E(Zn)= infinity


Expert Answer

Step 1


For a particular value of n, P (Zn = n2) = 1/n and P (Zn = 0) = 1 – 1/n.

Step 2


The expectation, as n tends to infinity, ...


Image Transcriptionclose

For a particular E(Ζ,) - Σ-Ρ(Ζ, = 3.) - 0- =n As n tends to infinity: lim E(Z,) lim(n) n0 n- That is. lm E(Z)». (Proved)


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