quiz3_Prac - 1000(b If the variance of a hour’s...

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ST561: Study problems for Quiz #3 1. Let X have a Uniform(0,1) distribution. (a) Use Chebyshev’s inequality to find a bound for P ( | X - 1 / 2 | ≥ 0 . 35). (b) Find the exact of P ( | X - 1 / 2 | ≥ 0 . 35). (c) Find the p.d.f. of Y = e X . (Be sure to specify the support of Y ). (d) Find E ( Y ) and use Jensen’s inequality to show that 1 / 2 ln( e - 1). (Here ln is natural logarithm). 2. Suppose it is known that the number of widgets produced for Guinness breweries in a factory during an hour is a random variable with mean 500. (a) What can be said about the probability that an hour’s production will exceed
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Unformatted text preview: 1000? (b) If the variance of a hour’s production is known to be 100, then what can be said about the probability that a hour’s production will be between 450 and 550? (c) What can be said about the probability that at least 550 widgets are made, assuming the mean is 500 and variance is 100? 3. Let X follow the exponential ( α,β ) distribution with pdf f ( x ) = 1 β e-( x-α ) /β for α < x < ∞ . Let Y = bX + a for some constants a and b with b > 0. Find the pdf of Y 1...
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