(a) Verify that fx,y is indeed a probability density function. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=x.
(a) Verify that fx,y is indeed a probability density function. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=x.
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.CR: Chapter 13 Review
Problem 30CR
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Transcribed Image Text:Question 1
function given by
Suppose that X and Y have a joint probability density
if x, y ≥ 0
otherwise
fx,y(x, y) =
(a) Verify that fx,y is indeed a probability density function.
(b) Find the marginal probability density function fx and state the name of the
distribution of X.
7e-x-7y
(c) Find the conditional probability density function fy|x=x-
(d) Are the random variables X and Y independent? Justify your answer.
(e) Let another probabilty density fx,y be given by
Sce-(√+√y)²+2√y
- {e
fx.y (x, y) =
if x ≥ y ≥0
otherwise
Determine the normalization constant c in this case. Are X and Y statistically
independent? Justify your answer.
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Can you please attempt part d and e
Transcribed Image Text:Question 1
function given by
Suppose that X and Y have a joint probability density
if x, y ≥ 0
otherwise
fx,y(x, y) =
(a) Verify that fx,y is indeed a probability density function.
(b) Find the marginal probability density function fx and state the name of the
distribution of X.
7e-x-7y
(c) Find the conditional probability density function fy|x=x-
(d) Are the random variables X and Y independent? Justify your answer.
(e) Let another probabilty density fx,y be given by
Sce-(√+√y)²+2√y
- {e
fx.y (x, y) =
if x ≥ y ≥0
otherwise
Determine the normalization constant c in this case. Are X and Y statistically
independent? Justify your answer.
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