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 xex/ 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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 Fall '08
 Castro
 Probability, Probability theory, 1%, Cumulative distribution function, 365 days, 300 days

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