I am trying to calculate a CDF of a random variable $x$ which has an upper bound $z$, which is itself a random variable with distribution $G(z)$ on some interval $[z1,z2]$.
E.g. $x \sim U[0,z]$ and $z \sim U[1,2]$.
I am trying to calculate a CDF of a random variable $x$ which has an upper bound $z$, which is itself a random variable with distribution $G(z)$ on some interval $[z1,z2]$.
E.g. $x \sim U[0,z]$ and $z \sim U[1,2]$.
The conditional pdf of $X$ given $Z$ is $f(x|z)=\frac{1}{z}\mathbb{I}[0
You can proceed by integrating it to get the CDF of $X$. You need to consider two different conditions when $x > 1$ and $x < 1$.