12. Grouping multinomial categories. Suppose that counts (N₁,..., Nm) are the num- bers of results in m categories in n

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12 Grouping Multinomial Categories Suppose That Counts N Nm Are The Num Bers Of Results In M Categories In N 1 (68.85 KiB) Viewed 7 times

Here is example 7 if you need Thank you!

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12. Grouping multinomial categories. Suppose that counts (N₁,..., Nm) are the num- bers of results in m categories in n repeated trials. So (N₁,..., Nm) has multinomial distribution with parameters n and p₁,...,pm, as in the box above Example 7. Let 1 ≤ i ≤ j ≤ m. Answer the following questions with an explanation, but no calcula- tion. a) What is the distribution of N₁? b) What is the distribution of N₂ + Nj? c) What is the joint distribution of N₁, N₁, and n – N₂ - Nj?
Example 7. Fours, fives, and sixes. Suppose a fair die is rolled 10 times, and the numbers of rolls of four, five, and six are recorded. Chapter 3. Random Variables Solution. From the multinomial distribution for n = 10 trials, m = 4 categories ("four", "five", "six", and "other") with probabilities 1/6, 1/6, 1/6 and 3/6, the required probability is P(Nfour 1, Nfive = 2, Nsix = 3, Nother = = 4) = 2 3 4 10! () * '()*()* 1!2!3!4!