Need help with this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable. 4.4-1. Let f(x, y) = (3/16)xy2, 0≤x≤ 2,0 ≤ y ≤ 2, bethe joint pdf of X and Y.(a) Find fx(x) and fy(y), the marginal probability densityfunctions.(b) Are the two random variables independent? Why orwhy not?(c) Compute the means and variances of X and Y.(d) Find P(X ≤ Y). 4.4-1 (a) fx(x) = x/2, 0≤x≤2: fy(y) = 3y²/8, 0≤ y ≤2;(b) Yes, because fx(x)fy(y) = f(x,y);(c) x = 4/3: y = 3/2; o(d) 3/5.= 2/9:03 = 3/20;

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4.4-1. Let f(x, y) = (3/16)xy²,0 ≤ x ≤ 2,0 ≤ y ≤ 2, be the joint pdf of X and Y. (a) Find fx(x) and fr(y), the marginal probability density functions. (b) Are the two random variables independent? Why or why not? (c) Compute the means and variances of X and Y.

4.4-1. Let f(x, y) = (3/16)xy²,0 ≤ x ≤ 2,0 ≤ y ≤ 2, be the joint pdf of X and Y. (a) Find fx(x) and fr(y), the marginal probability density functions. (b) Are the two random variables independent? Why or why not? (c) Compute the means and variances of X and 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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Question

Need help with this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable.

4.4-1. Let f(x, y) = (3/16)xy2, 0≤x≤ 2,0 ≤ y ≤ 2, be
the joint pdf of X and Y.
(a) Find fx(x) and fy(y), the marginal probability density
functions.
(b) Are the two random variables independent? Why or
why not?
(c) Compute the means and variances of X and Y.
(d) Find P(X ≤ Y).

4.4-1 (a) fx(x) = x/2, 0≤x≤2: fy(y) = 3y²/8, 0≤ y ≤
2;
(b) Yes, because fx(x)fy(y) = f(x,y);
(c) x = 4/3: y = 3/2; o
(d) 3/5.
= 2/9:03 = 3/20;

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