4.3 A certain genetic model suggest that the probabilities for a particular trinomial distribution are, respectively, u1 ¼ p2, u2 ¼ 2p(1  p), and u3 ¼ (1  p)2, 0 < p < 1. Assume that X1, X2, and X3 represent the respective frequencies in a sample of n independent trials and that these numbers are known. Derive a chi-square goodness-of-fit test for this trinomial distribution if p is unknown.