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1. Suppose that X, Y are discrete random variables (not necessarily indepen- dent) with joint PMF p(x,y) = P(X = x, Y = y). Show that the marginal PMF px(x) = P(X = x) of X can be obtained from the joint PMF p(x, y) by "summing away" Y. That is, for any given x, px (x) = [p(x,y). Hint: Use the Law of Total Probability. One of the sets in your partition will have probability 0.

1. Suppose that X, Y are discrete random variables (not necessarily indepen- dent) with joint PMF p(x,y) = P(X = x, Y = y). Show that the marginal PMF px(x) = P(X = x) of X can be obtained from the joint PMF p(x, y) by "summing away" Y. That is, for any given x, px (x) = [p(x,y). Hint: Use the Law of Total Probability. One of the sets in your partition will have probability 0.

A First Course in Probability (10th Edition)
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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Note: Similarly, we can also obtain py(y) by "summing away" X, PY (y) = [p(x,y). X Note: In the case of continuous random variables, the marginal PDFs can be found from the joint PDF, however then we must "integrate away" the unwanted random variable, fx (x) = f(x,y)dy fy (y) = f(x,y)dx.
Transcribed Image Text:Note: Similarly, we can also obtain py(y) by "summing away" X, PY (y) = [p(x,y). X Note: In the case of continuous random variables, the marginal PDFs can be found from the joint PDF, however then we must "integrate away" the unwanted random variable, fx (x) = f(x,y)dy fy (y) = f(x,y)dx.
1. Suppose that X,Y are discrete random variables (not necessarily indepen- dent) with joint PMF p(x,y) = P(X= x, Y = y). Show that the marginal PMF px(x) = P(X=x) of X can be obtained from the joint PMF p(x,y) by "summing away" Y. That is, for any given x, px (x) = [p(x,y). Hint: Use the Law of Total Probability. One of the sets in your partition will have probability 0.
Transcribed Image Text:1. Suppose that X,Y are discrete random variables (not necessarily indepen- dent) with joint PMF p(x,y) = P(X= x, Y = y). Show that the marginal PMF px(x) = P(X=x) of X can be obtained from the joint PMF p(x,y) by "summing away" Y. That is, for any given x, px (x) = [p(x,y). Hint: Use the Law of Total Probability. One of the sets in your partition will have probability 0.
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