Question: Question 7 (10 marks) Let X and Y be two independent random variables with marginal probability functions 1 y+1 fX(x) = ()x+1,x = 0,1,2, and

Question 7 (10 marks) Let X and Y be two independent random variables with marginal probability functions 1 y+1 fX(x) = ()x+1,x = 0,1,2, and My) 2 G) ,y = 0,1,2, 2 a) (1 mark) Find the joint probability function, fxy (x, y). b) (3 marks) Solve for E(XY). C) (3 marks) Find the probability function of T=X+Y. d) (3 marks) Find the conditional distribution of X given T=t, where T=X+Y

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Please help Q4. (10 marks) Let X1 and X2 be two independent random variables. Suppose each Xi is exponentially distributed with parameter ii. Let Y=Min (X1, X2). A) (5 marks) Find the pdf of Y. B) (5...

A comparative study is performed; you are given the following information. ? The total number of subjects equals 29. ? The observed value of the test statistic is greater than 0. I used the website...

Let X and Y be two continuous random variables with joint probability density function f(x, y) = 12 5 xy(1 + y) for 0 ? x ? 1 and 0 ? y ? 1, and f(x, y) = 0 otherwise. a. Find the probability P 1 4 ?...

EE 322 Probabilistic Methods for Electrical Engineers Homework 6 Assigned: 11/10. Due: 11/17 Problem 1. A digital communication system transmits a symbol S every T second. The symbol S is equal to...

Let X and Y be two continuous random variables with joint pdf f(x, y) = qx2 y(1 + y) for 0 x 3 and 0 y 3, and f(x, y) = 0 otherwise. (a)Find the value of q. (b) Find the probability P(1 X 2, 0 Y 1)....

1/ Let X1 and X2 be two independent random variables each with probability density function f Xi (xi) = e -xi , for x i > 0 for i = 1,2. (a) Find the joint probability density function of X1 and X2....

Please do the following exercises, showing all of your work. 1. Let X and Y be two independent random variables with densities fx (x) and fy(x). a) What is the joint density fix,ry(x, y)? b) Optional...

Based on Question $1, Let X, and Y be two independent random variables such that E(X)=2, Var(X)=4, E(Y)=7, and Var(Y)=1. Find: var(3X+7) A. 13 B. 9 C. 28 D. 36 OC OB OD OABased on Question 8, The...

Let X, and Y be two independent random variables such that E(X)=2, Var(X)=4, E(Y)=7. and Var(Y)=1. Find: E(3X+7) A. 13 B.19 C. 28 D. 6 O A OC OD O BLet X and Y be discrete random variables with joint...

The typical packet size of an IP packet including IPv4 header on 100 Mbps Ethernet is 1500 bytes. A typical IPv4 header consists of 20 bytes, and a UDP header consists of 8 bytes. If we split up a...

A training program should be designed and delivered. Students should include from designing and conducting effective interviews, including training in preparation, utilization of a structured...

When a bond is issued at a discount, the cash account is debited for Blank _ _ _ _ _ _ Multiple choice question. the face amount. more than the face amount. less than the face amount. the difference...

The following data are taken from the financial statements of Wildhorse Co. 2017 2016 Accounts receivable (net), end of year $588,600 $565,000 Net sales on account 4,862,000 4,148,000 Terms for all...