Given are the following possible values for h(X) in the different intervals:
$h(X)=0$ if $X\leq d$ and $h(X)=X$ if $X>d$.
Asked is to give the CDF of $h(X)$. Could you help me? The answer-book says for example that for $0 < x< d$, the cdf of $h(X)$ equals $1-e^{-d}$.
Thank you!
Something is missing here. Let $X$ be an positive random variable and $h(x)=0$ if $x \leq d$, $h(x)=x$ if $x >d$. Then the hypothesis is satisfied. For $0<x<d$ we have $P\{h(X)<x\}=P\{h(X)=0\}=P\{X\leq d\}$. This, of course, need not be any specific function of $d$. If you assume that your random variable $X$ has exponential distribution with parameter $d$ then the same calculation shows that $P\{h(X)<x\}=1-e^{-d}$ for $0<x<d$.