Can bounded (possibly continuous) random variable have infinite expectation? If no, how can we show it?
2026-03-25 11:09:02.1774436942
Can bounded random variable have infinite expectation?
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Hint: If a random variable $X$ is bounded, then $E[|X|] \le E[M] = M$ for some constant $M>0$ due to the monotonicity of the expectation. Write the second moment $E[X^2]$ and establish an upper bound in a similar way.