Exercise1.4 Consider apopulationwiththreekindsofindividualslabeled,say,1,2,and3occur-

ring inthefollowingproportions: p1 = p2, p2 = 2p(1−p), p3 = (1−p)2 (0 < p < 1). Inarandom sample ofsize n chosen fromthispopulation, n1 individualshavebeenlabeled1, n2—2 and n3—3 respectively(n1+n2+n3 = n).

1. Write downthelikelihoodfunction.

2. Does thedistributionofthedatabelongtotheexponentialfamily?Whatarethenaturalparameter and thesufficientstatistic?