I have two questions regarding to statistical distance in distributions.
1: If $Z$ is uniform random variable over $N$ consecutive integers and $m < N$ then $Z$ mod $m$ has statistical distance at most $m/N$ from the uniform distribution over $[m]$ ($[m] = {0,1,2,...m-1}$). How this statement is true based on the definition of statistical distance
2: For independent random variables $X_1, X_2, Y_1, Y_2$ the distance between the joint distributions $(X_1, X_2)$ and $(Y_1, Y_2)$ is at most the sum of statistical distances of $X_1$ from $Y_1$ and $X_2$ from $Y_2$. Similarly, if these variables are group elements in $G$, the statistical distance between $X_1$ ·$X_2$ and $Y_1$ ·$Y_2$ is no greater than the sum of statistical distances of $X_1$ from $Y_1$ and $X_2$ from $Y_2$. How can we prove this statement?
These questions are a part of the RSA accumulator paper by Dan Boneh et al. Thank you for your help.