A continuous random variable $X$ has the following probability distribution: $$ f(x)=4 x e^{-2 x}, \quad x>0 $$ a. Find the moment-generating function for $X$. b. Find the mean and variance of $X$.
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Step 1
Step 1: To find the moment-generating function for $X$, we need to calculate $M_X(t) = E[e^{tX}]$. Show more…
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