Expected Value and Variance of Exponential Random Variable
Problem 757
Let $X$ be an exponential random variable with parameter $\lambda$.
(a) For any positive integer $n$, prove that
\[E[X^n] = \frac{n}{\lambda} E[X^{n-1}].\]
(b) Find the expected value of $X$.
(c) Find the variance of $X$.
(d) Find the standard deviation of $X$.
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