Question
Let $f(x)=x e^{-x}$ if $x \geqslant 0$ and $f(x)=0$ if $x<0$(a) Verify that $f$ is a probability density function.(b) Find $P(1 \leqslant X \leqslant 2)$
Step 1
This means that the integral of $f(x)$ over its domain should be equal to 1. In mathematical terms, this is expressed as $\int_{-\infty}^{\infty} f(x) dx = 1$. Show more…
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