Question: Consider a random sequence X1, X2,, XN,. generated by the rule XN = N with probability 1N XN = 0 with probability 1 1N.

Consider a random sequence X1, X2,…, XN,…. generated by the rule XN = N with probability 1∕N XN = 0 with probability 1 − 1∕N.

(a) What is the expected value of XN?

(b) What is the variance of XN?

(c) What is the probability limit of XN as N → ∞?

(d) Comment.

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