180ahw4 - 3 Let f x = c sin x if x ∈(0 π and f x = 0...

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MATH 180A – Introduction to Probability Homework 4 (due 10/30/06) 1. Jimmy rides his old motorcycle every day of the year. The motorcycle starts with probability 1/2 each time Jimmy presses on the starter. Compute the probability that in a given year (365 days) Jimmy has to press the starter at least 3 times to start the motorcycle on more than 300 days. 2. A company sells packages containing 100 chips each. Each chip is defective with proba- bility 1%. Approximate the number of packages in a batch of 500 packages that contain 3 defective chips or more.
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Unformatted text preview: 3. Let f ( x ) = c sin( x ) if x ∈ (0 , π ) and f ( x ) = 0 otherwise. (a) What value of c makes f a PDF? (b) Suppose X is a random variable with f as PDF. Find its cumulative distribution function and compute E( X ). 4. Same as Problem 3 with f ( x ) = c xe-x/ 2 if x > 0 and f ( x ) = 0 if x ≤ 0. 5. Let a, c > 0 and de±ne f ( x ) = c/x 3 if x > a and f ( x ) = 0 if x ≤ a . Suppose f is a PDF. (a) Express c in terms of a . (b) Let X be a random variable with PDF f . Compute E( X ) as a function of a ....
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