Question

Q1) Two random variables X and Y with joint probability distribution function $f_{xy}(xy) = \frac{3}{2}x^2y^3$, for $0 \le x \le 2$, and $0 \le y \le 1$, calculate: 1. The two marginal probability distributions $f_x(x)$ and $f_y(y)$? 2. The variance $\sigma_x^2$ and $\sigma_y^2$? 3. The covariance $Cov(x, y)$? 4. The distribution $F(x,y)$? What is $F(2,1)$?

          Q1) Two random variables X and Y with joint probability distribution function $f_{xy}(xy) = \frac{3}{2}x^2y^3$, for $0 \le x \le 2$, and $0 \le y \le 1$, calculate:

1. The two marginal probability distributions $f_x(x)$ and $f_y(y)$?
2. The variance $\sigma_x^2$ and $\sigma_y^2$?
3. The covariance $Cov(x, y)$?
4. The distribution $F(x,y)$? What is $F(2,1)$?

Q1) Two random variables X and Y with joint probability distribution function fxy(xy) = (3)/(2)x^2y^3, for 0 ≤ x ≤ 2, and 0 ≤ y ≤ 1, calculate:

1. The two marginal probability distributions fx(x) and fy(y)?
2. The variance ^2 and ^2?
3. The covariance Cov(x, y)?
4. The distribution F(x,y)? What is F(2,1)?

Added by Concepci-N F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

01/25/2023

Step 1

Step 1: To find the marginal probability distribution fx(x), we integrate the joint probability distribution function fxy(xy) over all possible values of y. Show more…

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Q1) Two random variables X and Y with joint probability distribution function fxy(xy) = 323 2 x²y³, for 0 ≤ x ≤ 2, and 0 ≤ y ≤ 1, calculate: 1. The two marginal probability distributions fx(x) and fy(y)? 2. The variance σε and σ? 3. The covariance Cov(x, y)? 4. The distribution F(x,y)? What is F(2,1)?