Homework Help is Here – Start Your Trial Now!
Math
Probability
Suppose that in a particular year, STA3703 had three assignments in total. The summary of the marks obtained by civil engineering students at the three assignments is given as follows: Mean vector: Assignment number 1 2 3 Mean 72 60 64 The variance-covariance matrix: Assignment 1 Assignment 2 Assignment 3 Assignment 1 Assignment 2 Assignment 3 15 4 0 4 0 (ii) the distribution of the sum of the three assignments. 9 16 Let the random variable y be the vector of the marks obtained by a student at one of the assignments with Y₁, the mark obtained at assignment 1, Y₂ is the mark obtained at assignment 2 and Y3 is the mark obtained at assignment 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (iii) the joint pdf of assignment 1 and assignment 2 marks. 16 25

Suppose that in a particular year, STA3703 had three assignments in total. The summary of the marks obtained by civil engineering students at the three assignments is given as follows: Mean vector: Assignment number 1 2 3 Mean 72 60 64 The variance-covariance matrix: Assignment 1 Assignment 2 Assignment 3 Assignment 1 Assignment 2 Assignment 3 15 4 0 4 0 (ii) the distribution of the sum of the three assignments. 9 16 Let the random variable y be the vector of the marks obtained by a student at one of the assignments with Y₁, the mark obtained at assignment 1, Y₂ is the mark obtained at assignment 2 and Y3 is the mark obtained at assignment 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (iii) the joint pdf of assignment 1 and assignment 2 marks. 16 25

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
Suppose that in a particular year, STA3703 had three assignments in total. The summary of the marks obtained by civil engineering students at the three assignments is given as follows: Mean vector: The variance-covariance matrix: Assignment number Mean | Assignment 1 Assignment 2 Assignment 3 72 Assignment 1 15 4 2 60 Assignment 2 4 9 16 3 64 Assignment 3 16 25 Let the random variable Y be the vector of the marks obtained by a student at one of the assignments with Y1, the mark obtained at assignment 1, Y2 is the mark obtained at assignment 2 and Y3 is the mark obtained at assignment 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the distribution of the sum of the three assignments. (iii) the joint pdf of assignment 1 and assignment 2 marks. (iv) the covariance of X1 and X2 where X, is the sum of the marks obainted at the three assignments, and X2 is the difference between “the sum of the first two assignments" and "assignment 3", i.e. (v) the correlation of X1 and X, given in (iv). (b) Identify the distribution of (a)(iii).
Transcribed Image Text:Suppose that in a particular year, STA3703 had three assignments in total. The summary of the marks obtained by civil engineering students at the three assignments is given as follows: Mean vector: The variance-covariance matrix: Assignment number Mean | Assignment 1 Assignment 2 Assignment 3 72 Assignment 1 15 4 2 60 Assignment 2 4 9 16 3 64 Assignment 3 16 25 Let the random variable Y be the vector of the marks obtained by a student at one of the assignments with Y1, the mark obtained at assignment 1, Y2 is the mark obtained at assignment 2 and Y3 is the mark obtained at assignment 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the distribution of the sum of the three assignments. (iii) the joint pdf of assignment 1 and assignment 2 marks. (iv) the covariance of X1 and X2 where X, is the sum of the marks obainted at the three assignments, and X2 is the difference between “the sum of the first two assignments" and "assignment 3", i.e. (v) the correlation of X1 and X, given in (iv). (b) Identify the distribution of (a)(iii).
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS