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Unformatted text preview: wise she will go away alone. If Julia waits for T hour in the coﬀeeshop, ﬁnd (a) the cdf of T and (b) E ( T ). 1 4. [2 × 5 = 10 pts] Let X be a random variable with distribution function F ( x ) = (1 / 4) e x1 if∞ < x < 1 1 / 2 if 1 ≤ x < 2 x/ 4 if 2 ≤ x < 3 1 if x ≥ 3 . (a) Is X discrete, continuous or mixed? (b) Find P (0 < X ≤ 1 . 5). (c) Find P ( X = 3). (d) Find P (1 ≤ X < 3). (e) Find P (1 ≤ X ≤ 1). 5. [2 + 3 = 5 pts] Suppose X has a normal distribution with mean 2 and variance 4. If Y = ( X2) / 2, (a) ﬁnd the PDF of Y . (b) Find P (2 ≤ X ≤ 2)? 2...
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 Fall '08
 WEBER
 Standard Deviation, Probability distribution, Probability theory, probability density function, Cumulative distribution function

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