Let X1,X2,… be a sequence of i.i.d. discrete random variables with the probability mass function P(X1=m)=begincases(loge2)^m/2(m!), & m=0,1,2,…, 0, & otherwise.endcases If Sn=X1+X2+cdots+Xn, then which one of the following sequences of random variables converges to 0 in probability?

Q8Section A (Section A)8 of 60

Sequence converging to zero in probability

Let $X_1,X_2,…$ be a sequence of i.i.d. discrete random variables with the probability mass function

$P(X_1=m)=\begin{cases}\dfrac{(\log_e2)^m}{2(m!)}, & m=0,1,2,…,\ 0, & \text{otherwise.}\end{cases}$

If $S_n=X_1+X_2+\cdots+X_n$ , then which one of the following sequences of random variables converges to $0$ in probability?

Pick an option to check your answer.

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