GATE 2021 PI – Question 47
A discrete random variable has $P(X=x)=1/2^x$, x = 1,2,… . Find E[X] (integer).
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Show answer and explanation
Correct answer: 2 to 2
Explanation
This is geometric with success probability 1/2 on positive integers, giving mean 1/p = **2**. Alternatively, use $\sum_{x\ge1}xr^x=r/(1-r)^2$ at r = 1/2.