For a multinomial distribution with and , verify that Hint Use the binomial theorem (see Theoretical Exercise 4 38) to expand the sum a (b c) 2 , then substitute the binomial expansion of (b c) 2 in the resulting expression Finally, substitute a p 1 , b p 2 , and c p 3 ...

Calculation For a multinomial distribution with and we have p1p2p31 p21p22p231 ...

For a multinomial distribution with and , verify that [Hint: Use the binomial theorem (see Theoretical Exercise

Question:

For a multinomial distribution with and , verify that [Hint: Use the binomial theorem (see Theoretical Exercise 4.38) to expand the sum [a + (b + c)]² , then substitute the binomial expansion of (b + c)² in the resulting expression. Finally, substitute a = p₁, b = p₂, and c = p₃.]

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