5. (Sec. 5.1) Suppose the marginal pdfs of two independent rvs X and Y are given by 5x4 for 0 |0 otherwise 1 fx(r) 2y3for 0y <1 |0 otherwise fy(y) (a) Find the joint pdf of X and Y (b) What is the probability that both X and Y are greater than .5? (c) What is the probability that at least one of X or Y is greater than .5?

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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5. (Sec. 5.1) Suppose the marginal pdfs of two independent rvs X and Y are given by
5x4 for 0
|0 otherwise
1
fx(r)
2y3for 0y <1
|0 otherwise
fy(y)
(a) Find the joint pdf of X and Y
(b) What is the probability that both X and Y are greater than .5?
(c) What is the probability that at least one of X or Y is greater than .5?
Transcribed Image Text:5. (Sec. 5.1) Suppose the marginal pdfs of two independent rvs X and Y are given by 5x4 for 0 |0 otherwise 1 fx(r) 2y3for 0y <1 |0 otherwise fy(y) (a) Find the joint pdf of X and Y (b) What is the probability that both X and Y are greater than .5? (c) What is the probability that at least one of X or Y is greater than .5?
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