Chapter 4.3, Problem 4E

The gene for eye color in a certain male fruit fly has alleles $\left(R,W\right)$.

The gene for eye color in the mating female fruit fly also has alleles $\left(R,W\right)$.

Their offspring receive one allele for eye color from each parent. If an offspring ends up with either $\left(R,R\right),\left(R,W\right),$ or $\left(W,R\right)$, its eyes will look red. Let X equal the number of offspring having red eyes. Let V equal the number of red-eyed offspring having $\left(R,W\right)$ or $\left(W,R\right)$ genes.

(a) If the total number of offspring is $n=400$, how is X distributed?

(b) Give the values of E(X) and Var(X).

(c) that $X=300$, how is Y distributed.

(d) Give the values of $E\left(Y|X=X\right)$ and $Var\left(Y|X=300\right)$.