1. Suppose $X$ and $Y$ are independent random variables, each uniformly distributed on $(0, 1)$. Find the probability density function of $Z = XY$.
2. Suppose $X$ and $Y$ are independent binomial random variables, each with probability of success $p$. Suppose $X$ has $n$ trials and $Y$ has $m$ trials. Use the convolution of the probability mass functions to show that $X + Y$ is binomial with $n + m$ trials and probability of success $p$.

Problems: 7.22, 7.38

This Problem Set is due at the beginning of class, Monday, 18 November.