11. Random variable and have the following joint probability distribution. f(x,y) y 1 2 3 x 1 2 3 0.1 0.1 0.15 0.05 0.05 0.2 0.15 0.1 0.1 a) Find P(X + Y ≤ 4). b) Find the marginal probability distributions f₁ (x) and f₂ (y). c) Find P(X < 2|Y = 2). d) Are X and Y independent? e) Find E(X) and E(Y), Var(X) and Var(Y). f) Find the correlation coefficient of X and Y.
11. Random variable and have the following joint probability distribution. f(x,y) y 1 2 3 x 1 2 3 0.1 0.1 0.15 0.05 0.05 0.2 0.15 0.1 0.1 a) Find P(X + Y ≤ 4). b) Find the marginal probability distributions f₁ (x) and f₂ (y). c) Find P(X < 2|Y = 2). d) Are X and Y independent? e) Find E(X) and E(Y), Var(X) and Var(Y). f) Find the correlation coefficient 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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Transcribed Image Text:11. Random variable and have the following joint probability distribution.
f(x,y)
y
1
2
3
1 2 3
0.1 0.1 0.15
0.2
0.05 0.05
0.15 0.1 0.1
a) Find P(X + Y ≤ 4).
b) Find the marginal probability distributions f₁ (x) and f₂ (y).
c) Find P(X < 2|Y = 2).
d) Are X and Y independent?
e) Find E(X) and E(Y), Var(X) and Var(Y).
f) Find the correlation coefficient of X and Y.
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