A continuous random variable has a p.d.f $f(x)=k x^{2} e^{-x}, x \geq 0$. Find k and mean.
Explanation
The given p.d.f is a gamma distribution with shape parameter 3 and scale parameter 1. The mean of a gamma distribution is given by: \mu = \alpha \beta = 3 \cdot 1 = 3.
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