For the multinomial (n,{Ï€_j}) distribution with c > 2, confidence limits for Ï€_jare the solutions of 

a. Using the Bonferroni inequality, argue that these c intervals simultaneously contain all {Ï€_j} (for large samples) with probability at least 1€“ α.

b. Show that the standard deviation of π̂_j €“ π̂_k is [Ï€_j + Ï€_k €“ (Ï€_j €“ Ï€_k)²]/n. For large n, explain why the pfrobability is at least 1 €“ α that the Wald confidence intervals.

Simultaneously contain the a = c(c €“ 1)/2 differences {Ï€_j €“ Ï€_k}

(, T,)' = (za/pe) 7,(1 7,)/n, j = 1, ..., c. | (, - ) 2a/2 .{[i) + ; - () - .)}]/^}" 1/2