Let the joint p.m.f. of X and Y be defined by 3x + y 45 f(x, y) = x = 1,2,3 y = 1,2 a) Find fx(r), the marginal p.m.f. of X, and fy(y), the marginal p.m.f. of Y. b) Are X and Y independent? Please explain your reasoning. c) Find P(X + Y <4).
Let the joint p.m.f. of X and Y be defined by 3x + y 45 f(x, y) = x = 1,2,3 y = 1,2 a) Find fx(r), the marginal p.m.f. of X, and fy(y), the marginal p.m.f. of Y. b) Are X and Y independent? Please explain your reasoning. c) Find P(X + Y <4).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Exercise on Joint Probability Mass Function**
Let the joint probability mass function (p.m.f.) of random variables \(X\) and \(Y\) be defined by:
\[
f(x, y) = \frac{3x + y}{45}, \quad x = 1, 2, 3 \quad y = 1, 2
\]
**Questions:**
a) Find \( f_X(x) \), the marginal p.m.f. of \( X \), and \( f_Y(y) \), the marginal p.m.f. of \( Y \).
b) Are \( X \) and \( Y \) independent? Please explain your reasoning.
c) Find \( P(X + Y < 4) \).
**Note:** There are no graphs or diagrams included in this text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18574973-f25e-4ab8-b7d6-6007b5b87fc4%2F4eb99405-1cb6-40ed-b133-2d9b32ff8e54%2Fr0qnshh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise on Joint Probability Mass Function**
Let the joint probability mass function (p.m.f.) of random variables \(X\) and \(Y\) be defined by:
\[
f(x, y) = \frac{3x + y}{45}, \quad x = 1, 2, 3 \quad y = 1, 2
\]
**Questions:**
a) Find \( f_X(x) \), the marginal p.m.f. of \( X \), and \( f_Y(y) \), the marginal p.m.f. of \( Y \).
b) Are \( X \) and \( Y \) independent? Please explain your reasoning.
c) Find \( P(X + Y < 4) \).
**Note:** There are no graphs or diagrams included in this text.
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