1. The discrete random variables X and Y have known joint probability mass function C x = 0,1,2,L,9, y = 0,1,2,L,9, y≥x otherwise where c is a Pxy(x, y) given by Py(x, y) = constant. a) Determine the value of the constant c that makes the above Pxy(x, y) a valid joint probability mass function. b) Determine the marginal probability mass functions Px(x) and Py(y). Are the random variables statistically independent? c) Determine the covariance cov(X,Y) of the random variables X and Y. d) Determine the correlation coefficient Px of the random variables X and Y c) Is the expected value E{XY} equal to E{X}E{Y}? Explain why it is or why it is not. 3
1. The discrete random variables X and Y have known joint probability mass function C x = 0,1,2,L,9, y = 0,1,2,L,9, y≥x otherwise where c is a Pxy(x, y) given by Py(x, y) = constant. a) Determine the value of the constant c that makes the above Pxy(x, y) a valid joint probability mass function. b) Determine the marginal probability mass functions Px(x) and Py(y). Are the random variables statistically independent? c) Determine the covariance cov(X,Y) of the random variables X and Y. d) Determine the correlation coefficient Px of the random variables X and Y c) Is the expected value E{XY} equal to E{X}E{Y}? Explain why it is or why it is not. 3
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.1: Continuous Probability Models
Problem 28E
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Step 1: Write the given information.
VIEWStep 2: Determine value of constant c that makes the above PXY(x,y) a valid joint probability mass function.
VIEWStep 3: Determine the marginal probability mass functions Px(x) and Py(y).
VIEWStep 4: Determine the covariance cov(X,Y) of the random variables X and Y.
VIEWStep 5: Determine the correlation coefficient of the random variable X and Y.
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