April 9th, 2018, 07:50 PM #1 Newbie   Joined: Apr 2018 From: Canada Posts: 3 Thanks: 0 Joint PMF of Multivariate A class contains 6 freshmen, 15 sophomores, 12 juniors and 7 seniors. Suppose that a random sample of 5 students is taken with replacement. Let x1; x2; x3; and x4 denotes the number of freshmen, sophomores, juniors, and seniors, respectively, obtained. a) Identify and determine the joint pmf ofx1;x2;x3andx4. Use part a) and the FPF to determine the probability the sample contains: b) no freshmen, 3 sophomores, 1 junior and 1 senior. c) at least 3 sophomores. d) at least 3 sophomores and at least one junior April 10th, 2018, 12:38 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,468 Thanks: 1342 This is a multinomial distribution. let $p = \dfrac{1}{40}(6,~15,~12,~7)$ $p[x_1,x_2,x_3,x_4] = \dfrac{5!}{\prod \limits_{k=1}^4~x_k!} \cdot \prod \limits_{k=1}^4~(p_k)^{x_k}$ for b-d create a list of selections that match the criteria, find the probability of each using the formula above, and sum them up to find the probability of satisfying the criteria. Thanks from Shima Last edited by romsek; April 10th, 2018 at 01:27 AM. April 10th, 2018, 11:41 AM   #3
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Multinomial

Can you, however, help me with the part C and D?

Quote:
 Originally Posted by romsek This is a multinomial distribution. let $p = \dfrac{1}{40}(6,~15,~12,~7)$ $p[x_1,x_2,x_3,x_4] = \dfrac{5!}{\prod \limits_{k=1}^4~x_k!} \cdot \prod \limits_{k=1}^4~(p_k)^{x_k}$ for b-d create a list of selections that match the criteria, find the probability of each using the formula above, and sum them up to find the probability of satisfying the criteria. April 10th, 2018, 12:19 PM   #4
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Quote:
 Originally Posted by Shima Can you, however, help me with the part C and D?
you can't list the groupings that satisfy the criteria for c and d and plug the numbers in?

c will be any selection with 3, 4, or 5 sophmores

d will be any selections with 1 junior and 3 or 4 sophmores

I have great faith in your ability to list these out and chug the numbers.

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