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# Ex5 - reaching the station the person needs 2 minutes to...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306: INTRODUCTORY STATISTICS Sem 1 2008/2009 EXAMPLE CLASS 5 Q1. f ( x ) = ( ρ - 1) x - ρ for x 1 , ρ > 1 0 otherwise a) Is f(x) a density function? Why? b) Find F(x). Q2. Let the p.d.f. of X be f ( x ) = 1 - | x - 1 | for 0 x 2 . (a) Sketch f ( x ). (b) Find the distribution function of X . 1

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Q3. Let X have the p.d.f. f ( x ) = e - x - 1 for - 1 x < . (a) Find P ( X 1). (b) Find the distribution function F ( x ). Q4. Let X have the p.d.f. f ( x ) = 1 π (1 + x 2 ) for -∞ < x < Find the distribution function F ( x ). 2
Q5. A person who wants to catch a 6pm train takes a taxi at 5:43pm from an intersection that under ideal driving conditions is 10 minutes from the MTR station, but which can be as much as 50 minutes driving time away from the station if traffic is heavy. Assume that X U [10 , 50] where X is the driving time from the intersection to the station, and assume that upon

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Unformatted text preview: reaching the station, the person needs 2 minutes to board the train. Thus if a person is to catch the train, X must be no greater than 15 minutes. (a) What is the pdf? Draw a sketch. (b) Find the cdf. Draw a sketch. (c) What is the probability that the person catches the train? 3 Q6. Mueller (1950) describes an experiment in which white rats were peri-odically conditioned.The duration of time in seconds between presses by a rat on a bar has an exponential distribution with parameter θ = 0 . 2 . (a) What is the pdf? Draw a rough sketch. (b) Find the cdf. Draw a rough sketch. (c) Find the probability that it takes a rat between 1 and 3 seconds to press the bar. 4...
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