Suppose that in a particular year, STA3703 had three assignments in total. The summary of the marks obtained bycivil engineering students at the three assignments is given as follows:Mean vector:The variance-covariance matrix:Assignment number Mean| Assignment 1 Assignment 2 Assignment 372Assignment 1154260Assignment 24916364Assignment 31625Let the random variable Y be the vector of the marks obtained by a student at one of the assignments with Y1, themark obtained at assignment 1, Y2 is the mark obtained at assignment 2 and Y3 is the mark obtained at assignment3.(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).

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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...

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