4.4-1 a and c only ### Exercises#### 4.4-1. Let $ f(x, y) = (3/16)xy^2 $, $ 0 \leq x \leq 2 $, $ 0 \leq y \leq 2 $, be the joint pdf of $ X $ and $ Y $.(a) Find $ f_X(x) $ and $ f_Y(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 \leq Y) $.#### 4.4-2. Let $ X $ and $ Y $ have the joint pdf $ f(x, y) = x + y $, $ 0 \leq x \leq 1 $, $ 0 \leq y \leq 1 $.(a) Find the marginal pdfs $ f_X(x) $ and $ f_Y(y) $ and show that $ f_Y(y) \neq f_X(y) $. Then find $ P(X \leq Y) $.(Note: No graphs or diagrams are present in the provided content.)

Name: 4.4-1 a and c only ### Exercises#### 4.4-1. Let $ f(x, y) = (3/16)xy^
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Description: 4.4-1 a and c only ### Exercises#### 4.4-1. Let \( f(x, y) = (3/16)xy^2 $, $ 0 \leq x \leq 2 $, $ 0 \leq y \leq 2 $, be the joint pdf of $ X $ and $ Y $.(a) Find $ f_X(x) $ and $ f_Y(y) $, the marginal probability density functions.(b) A

Given that, the joint pdf of X and Y is fx,y=316xy2 , 0≤x≤2, 0≤y≤2 The Marginal probability,…

Answered: (a) Find fy(x) and fy(y), the marginal…

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Probability

(a) Find fy(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.

A First Course in Probability (10th Edition)

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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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4.4-1 a and c only

### Exercises

#### 4.4-1. Let $ f(x, y) = (3/16)xy^2 $, $ 0 \leq x \leq 2 $, $ 0 \leq y \leq 2 $, be the joint pdf of $ X $ and $ Y $.

(a) Find $ f_X(x) $ and $ f_Y(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 \leq Y) $.

#### 4.4-2. Let $ X $ and $ Y $ have the joint pdf $ f(x, y) = x + y $, $ 0 \leq x \leq 1 $, $ 0 \leq y \leq 1 $.

(a) Find the marginal pdfs $ f_X(x) $ and $ f_Y(y) $ and show that $ f_Y(y) \neq f_X(y) $. Then find $ P(X \leq Y) $.

(Note: No graphs or diagrams are present in the provided content.)

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