The alleles for eye color in a certain male fruit fly are (R, W). The alleles fo

Question

The alleles for eye color in a certain male fruit fly are (R, W). The alleles for eye color in the mating female fruit fly are (R, W). Their offspring receive one allele for eye color from each parent. If an offspring ends up with either (W, W), (R, W), or (W, R), its eyes will look white. Let X equal the number of offspring having white eyes. Let Y equal the number of white-eyed offspring having (R, W) or (W, R) alleles (a) If the total number of offspring is n = 400, how is X distributed? (b) Give the values of E(X) andVar(X) (c) Given that X= 300, how is Y distributed? (d) Give the value of E(Y IX = 300) and the value of Var(YP: 300).

Explanation / Answer

(a) Here number of offspring n = 400

The X is distributed binomial. where n = 400 and p = 0.75

so it is a binomial distribution.

(b) E(X) = np = 400 * 0.75 = 300

Var(X) = npq = (400 * 0.25 * 0.75) = 75

(c) X = 300,

so there is 2/3 probability that number of white-eyes offspring having (R,W) or (W,R) alleles.

here n = 300 and p = 2/3

(d) E(Y l X = 300) = 300 * 2/3 = 200

Var(Y l X = 300) = 300 * 2/3 * 1/3 = 200/3 = 66.6667

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