1.33 For testing Ho: ; = jo, j = 1,..., c, using sample multinomial proportions {;}, the likelihood-ratio statistic (1.17) is 2 G = 2

1.33 For testing Ho: π; = πjo, j = 1,...,

c, using sample multinomial proportions {;}, the likelihood-ratio statistic (1.17) is 2

G² = −2η Σπ; log(njo/nj).

j j

Show that G² ≥ 0, with equality if and only if ₁ = πjo for all j. [Hint: Apply Jensen's inequality to E(-2n log X), where X equals πο/π; with probability ;.]