3. Let X and Y be discrete random variables with the following joint probability function. X Y f(x,y) = P(X=x,Y=y) 2 4 0.15 2 7 0.25 11 4 0.32 7 0.28 E 11 (a) Is the above a valid PMF? Verify (b) Using the table above find the expected value of X, E[X]. (c) Using the table above find the expected value of Y, E[Y]. (d) Using the table above find the expected value of XY, E[XY]. (e) Determine the covariance of XY, note Cov(X,Y)= E[XY] − E[X] * E[Y].
3. Let X and Y be discrete random variables with the following joint probability function. X Y f(x,y) = P(X=x,Y=y) 2 4 0.15 2 7 0.25 11 4 0.32 7 0.28 E 11 (a) Is the above a valid PMF? Verify (b) Using the table above find the expected value of X, E[X]. (c) Using the table above find the expected value of Y, E[Y]. (d) Using the table above find the expected value of XY, E[XY]. (e) Determine the covariance of XY, note Cov(X,Y)= E[XY] − E[X] * E[Y].
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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Hi. I only need help for questions d) and e) please.
![3. Let X and Y be discrete random variables with the following joint probability function.
X
Y f(x,y) = P(X=x,Y=y)
2
4
0.15
2
7
0.25
11 4 0.32
7
0.28
E
11
(a) Is the above a valid PMF? Verify
(b) Using the table above find the expected value of X, E[X].
(c) Using the table above find the expected value of Y, E[Y].
(d) Using the table above find the expected value of XY, E[XY].
(e) Determine the covariance of XY, note Cov(X,Y) = E[XY] − E[X] * E[Y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8b48535-184f-4977-af2d-d816dbce40fd%2Fa25273a6-0ed6-4745-a36f-9228b964b980%2Ftj2uoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let X and Y be discrete random variables with the following joint probability function.
X
Y f(x,y) = P(X=x,Y=y)
2
4
0.15
2
7
0.25
11 4 0.32
7
0.28
E
11
(a) Is the above a valid PMF? Verify
(b) Using the table above find the expected value of X, E[X].
(c) Using the table above find the expected value of Y, E[Y].
(d) Using the table above find the expected value of XY, E[XY].
(e) Determine the covariance of XY, note Cov(X,Y) = E[XY] − E[X] * E[Y].
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