TIFR ECE 2015 | Question: 10

Question

Let $X$ be a uniform random variable between $[0,1]$. And let
\[
M=\min _{m X \geq 1, m \in \mathbb{N}} m .
\]
Then which of the following is true?

• A. $E(M)=\infty$
• B. $E(M) \in[5,10]$
• C. $E(M)=\exp (1)$
• D. $E(M)=\pi$
• E. None of the above