4. Are X and Y independent? Why? 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).
4. Are X and Y independent? Why? 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).
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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sub questions 4 and 5 please
Transcribed Image Text:Suppose two random variables X and Y have a joint pdf
f (x, y) = {
where k is a positive constant.
1. Show that the joint cdf is given by:
k(1-y) 0<x<y<1
0
elsewhere
F(x, y) = k (²+²+
6
2. Find the value of k using the answer from question 1.
1-51²)
ry²
2
+ xy
3. Find the marginal pdfs fx(r), fy (y) and the marginal cdfs Fx(x), Fy(y).
4. Are X and Y independent? Why?
5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).
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