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Fall 2004

# Fall 2004 - 1 Stat 230 Final Exam Draft(total marks=126...

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1 Stat 230 Final Exam Draft (total marks=126) LONG ANSWER QUESTIONS (Total marks possible=74) [12] 1. Suppose X is a discrete uniform random variable with probability function f ( x )=1 / 4 ,x =1 , 2 , 3 , 4 .F ind (a) P ( X 2) (b) P ( X =2 | X 2) (c) Var( X )

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2 (d) the cumulative distribution function of X
3 [12] 2. Cars arrive at a border crossing according to a Poisson process at the rate of λ =2 per hour. (a) Find the probability that no cars arrive between 8:00 am and 11:00 am on a given day. (b) Suppose you know that 3 cars arrived between 7:00 am and 8:00 am on that day. How does that change your answer to part (a). Explain. (c) In 100 consecutive days, what is the probability that there are two or more days in which no cars arrive between 8:00 am and 11:00 am?

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4 (d) In 100 consecutive days, using an appropriate approximation, find the probability that the total number of cars arriving between 8:00 am and 11:00 am falls between 500 and 550
5 [12] 3. Three tags are selected at random without replacement from a set of 5 tags labeled a, b, c, d, e .L e t A be the event that tag a is selected and D the eventthattag d is selected. (a) Find P ( A ¯ D ) (b) Are the events A and ¯ D independent? Explain. (c) Are the events A and ¯ D mutually exclusive? Explain. (d) Suppose X is the number of tags selected with a vowel ( a or e )label . Find the probability function for X .

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6 [8] 4. Numbers 11, 12, . ..,20 are written on 10 cards which are placed in a box.
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Fall 2004 - 1 Stat 230 Final Exam Draft(total marks=126...

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