We consider two urns each containing $A$ balls of which $pA$ are white and $qA$ are black. We draw simultaneously, in an equiprobable manner, $n$ balls from the first urn. We denote $Y$ the number of white balls obtained. We also draw, in an equiprobable manner, $n$ balls from the second urn, but successively and with replacement. We denote $Z$ the number of white balls obtained.
What is the distribution of the variable $Z$? Give the expectation and variance of $Z$.