Suppose that random variables ?1 and ?2 have exponential distribution with expected value of 1 2 and 1 3 , respectively. Assume that ?1 and ?2 are independent of each other. Find i) The joint density function of ?1 and ?2. ii) ?(?1 >1, ?2 > 1) iii) ?(?2 < 5)

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
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Suppose that random variables ?1 and ?2 have exponential distribution with expected value of
1
2 and 1
3 , respectively. Assume that ?1 and ?2 are independent of each other.
Find
i) The joint density function of ?1 and ?2.
ii) ?(?1 >1, ?2 > 1)
iii) ?(?2 < 5) 

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