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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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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