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Homework3

# Homework3 - and σ 4 Let X be a continuous random variable...

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ST561 Fall 2010 Homework 3 Due: Monday, Oct. 18th, 2010 1. Text Page 57, 1.6.3 2. Let f ( x ) be a p.d.f and let a be a number such that, for all ε > 0, f ( a + ε ) = f ( a - ε ). Such a p.d.f. is said to be symmetric about the point a . Show that if a random variable X has a p.d.f. which is symmetric about a , then the median of X equals to a . 3. Let X be distributed N ( μ, σ 2 ). Suppose the median of X is 50 and P ( X > 100) = 0 . 025. Can μ and σ be evaluated uniquely? If yes, find the values of
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Unformatted text preview: and σ ? 4. Let X be a continuous random variable with the p.d.f. f ( x ) and c.d.f. F ( x ). Find the c.d.f. and p.d.f of | X | . 5. Text Page 63, 1.7.21 6. Compute the mean and variance for random variables with each of the following p.d.f’s • f ( x ) = ax a-1 , for 0 < x < 1 and a > 0. • f ( x ) = (3 / 2)( x-1) 2 , for 0 < x < 2. 7. Text Page 94, 2.3.15. 8. Text Page 94, 2.3.16 1...
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