$n>0$ balls into $x \ge 2$ bins. X represents the number of balls landing in bin 1, and $Y$ the number of balls landing in bin 2.

Question

I'm having trouble solving this problem. I don't really know how to do it especially the last part.

We throw n>0 balls into x >= 2 bins. X represents the number of balls landing in bin1, and Y the number of balls landing in bin2.

• Calculate: E[X], E[Y], E[X|Y], Var(X), cov(X,Y)
• Calculate: L[X|Y], L[Y|X], Q[X|Y]? (where Q[X|Y] is the best quadratic estimator of Y given X, and L represents the Linear Least Square Estimate)

Answer 1

For 2 states you can easily convert this to a cointoss puzzle. For example if I toss n coins how many heads is same as how many will land in bin1. Similarly bin2 is tails. You can add more states easily