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Unformatted text preview: , 0 ≤ x ≤ 4, f ( x ) = 0, otherwise. a) What must the value of k be so that f ( x ) is a probability density function? b) Find the cumulative distribution function of X, F X ( x ) = P ( X ≤ x ). c) Find the probability P ( 1 ≤ X ≤ 2 ). d) Find the median of the distribution of X. That is, find m such that P ( X ≤ m ) = P ( X ≥ m ) = 1 / 2 . e) Find the 30th percentile of the distribution of X. That is, find a such that P ( X ≤ a ) = 0.30. f) Find μ X = E ( X ). g) Find σ X = SD ( X ). 2. Let X be a continuous random variable with the cumulative distribution function F ( x ) = 0, x < 0, F ( x ) = 8 3 ⋅ x , 0 ≤ x ≤ 2, F ( x ) = 1 – 2 1 x , x > 2. a) Find the probability density function f ( x ). b) Find the probability P ( 1 ≤ X ≤ 4 ). c) Find μ X = E ( X ). d) Find σ X = SD ( X )....
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 Spring '08
 Kim
 Probability, Probability theory, probability density function

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