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(f) Calculate E(X|Y = y), y = 1,2 and calculate E(E(X|Y)). (g) Compare E(X) and E(E(X|Y)). (h) Calculate the m.g.f. Mx,y.

(f) Calculate E(X|Y = y), y = 1,2 and calculate E(E(X|Y)). (g) Compare E(X) and E(E(X|Y)). (h) Calculate the m.g.f. Mx,y.

MATLAB: An Introduction with Applications
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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(f) Calculate \( E(X|Y = y) \), \( y = 1, 2 \) and calculate \( E(E(X|Y)) \). (g) Compare \( E(X) \) and \( E(E(X|Y)) \). (h) Calculate the m.g.f. \( M_{X,Y} \).
Transcribed Image Text:(f) Calculate \( E(X|Y = y) \), \( y = 1, 2 \) and calculate \( E(E(X|Y)) \). (g) Compare \( E(X) \) and \( E(E(X|Y)) \). (h) Calculate the m.g.f. \( M_{X,Y} \).
The joint probability density function (p.d.f) of the random variables (r.v.'s) X and Y is given in the following table: \[ \begin{array}{c|cccc} y\setminus x & 0 & 1 & 2 & 3 \\ \hline 1 & \frac{1}{8} & \frac{1}{16} & \frac{3}{16} & \frac{1}{8} \\ 2 & \frac{1}{16} & \frac{1}{16} & \frac{1}{8} & \frac{1}{4} \\ \end{array} \] Explanation: - The table represents the joint probability density function of the discrete random variables X and Y. - The columns represent the values of variable X: 0, 1, 2, and 3. - The rows represent the values of variable Y: 1 and 2. - Each cell in the table shows the joint probability for a specific pair of (X, Y) values.
Transcribed Image Text:The joint probability density function (p.d.f) of the random variables (r.v.'s) X and Y is given in the following table: \[ \begin{array}{c|cccc} y\setminus x & 0 & 1 & 2 & 3 \\ \hline 1 & \frac{1}{8} & \frac{1}{16} & \frac{3}{16} & \frac{1}{8} \\ 2 & \frac{1}{16} & \frac{1}{16} & \frac{1}{8} & \frac{1}{4} \\ \end{array} \] Explanation: - The table represents the joint probability density function of the discrete random variables X and Y. - The columns represent the values of variable X: 0, 1, 2, and 3. - The rows represent the values of variable Y: 1 and 2. - Each cell in the table shows the joint probability for a specific pair of (X, Y) values.
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