
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 2,042 Thanks: 1064 
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 bd 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. Last edited by romsek; April 10th, 2018 at 01:27 AM. 
April 10th, 2018, 11:41 AM  #3  
Newbie Joined: Apr 2018 From: Canada Posts: 3 Thanks: 0  Multinomial
Can you, however, help me with the part C and D? Quote:
 
April 10th, 2018, 12:19 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,042 Thanks: 1064  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. Use some software. 

Tags 
joint, multivariate, pmf 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Multivariate Brownian motion  calypso  Advanced Statistics  0  December 18th, 2016 02:45 AM 
Multivariate Calculus Help!  raininegypt  Calculus  1  June 15th, 2015 10:40 AM 
Multivariate differentiation  mitilma  Calculus  2  January 1st, 2014 04:31 AM 
Multivariate normal distribution  Nobody1111  Advanced Statistics  1  June 4th, 2011 01:35 PM 
Average of a multivariate function  hoffan  Computer Science  2  February 9th, 2010 12:43 PM 