Unformatted text preview: P ( X ≥ 3) and compare it to your answers in (a) and (b). (d) Use Jensen’s inequality to ﬁnd a lower bound for E ( e X ). (e) Calculate exactly E ( e X ) and compare it with your answer in (d). 4. Let X follows a Geometric distribution with parameter p . Let Y = X 2 + 1. Find the probability mass function of Y . 5. Let Y 1 and Y 2 be independent random variables and both follow the uniform distribu-tion on (0 , 1). Let U = Y 1 + Y 2 . Find the distribution function of U and the probability density function of U . 1...
View Full Document
- Fall '08
- Probability theory, probability density function, upper bound, Probability mass function, Geometric distribution