Question: Consider a random variable Zn with the probability distribution (a) Does Zn !p 0 as n!1? (b) Calculate E[Zn] . (c) Calculate var[Zn] . (d)

Consider a random variable Zn with the probability distribution

-n Zn = 0 n with probability 1/n with probability 1-2/n with

(a) Does Zn !p 0 as n!1?

(b) Calculate E[Zn] .

(c) Calculate var[Zn] .

(d) Now suppose the distribution is

probability 1/n.

Calculate E[Zn] .

(e) Conclude that Zn !p 0 as n!1and E[Zn]!0 are unrelated.

-n Zn = 0 n with probability 1/n with probability 1-2/n with probability 1/n.

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