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x²y Consider the joint probability mass function p(x, y) for x = 1, 2, 3 and y = 1,2,3 84 a) Build a table below containing the joint probabilities of X and Y, along with the marginal prob- abilities. b) choose a pair of values (x, y) and test whether px(x)py (y) PXY (x, y) (note: if they are not equal, we have proven that X and Y are dependent, but if they are equal, this is not yet enough to prove independence we would have to try every combination of x and y) = c) We can generate a formula for px(x) by taking the sum Σ3-1PXY (x, y) (note: this is just a restatement of the law of total probability). Similarly, py(y) = Σ¾³±1 Pxy(x, y). Find these functions and use them to prove that X and Y are independent.

x²y Consider the joint probability mass function p(x, y) for x = 1, 2, 3 and y = 1,2,3 84 a) Build a table below containing the joint probabilities of X and Y, along with the marginal prob- abilities. b) choose a pair of values (x, y) and test whether px(x)py (y) PXY (x, y) (note: if they are not equal, we have proven that X and Y are dependent, but if they are equal, this is not yet enough to prove independence we would have to try every combination of x and y) = c) We can generate a formula for px(x) by taking the sum Σ3-1PXY (x, y) (note: this is just a restatement of the law of total probability). Similarly, py(y) = Σ¾³±1 Pxy(x, y). Find these functions and use them to prove that X and Y are independent.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 20E
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x²y Consider the joint probability mass function p(x, y) for x = 1, 2, 3 and y = 1,2,3 84 a) Build a table below containing the joint probabilities of X and Y, along with the marginal prob- abilities. b) choose a pair of values (x, y) and test whether px(x)py (y) PXY (x, y) (note: if they are not equal, we have proven that X and Y are dependent, but if they are equal, this is not yet enough to prove independence we would have to try every combination of x and y) = c) We can generate a formula for px(x) by taking the sum Σ3-1PXY (x, y) (note: this is just a restatement of the law of total probability). Similarly, py(y) = Σ¾³±1 Pxy(x, y). Find these functions and use them to prove that X and Y are independent.
Transcribed Image Text:x²y Consider the joint probability mass function p(x, y) for x = 1, 2, 3 and y = 1,2,3 84 a) Build a table below containing the joint probabilities of X and Y, along with the marginal prob- abilities. b) choose a pair of values (x, y) and test whether px(x)py (y) PXY (x, y) (note: if they are not equal, we have proven that X and Y are dependent, but if they are equal, this is not yet enough to prove independence we would have to try every combination of x and y) = c) We can generate a formula for px(x) by taking the sum Σ3-1PXY (x, y) (note: this is just a restatement of the law of total probability). Similarly, py(y) = Σ¾³±1 Pxy(x, y). Find these functions and use them to prove that X and Y are independent.
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