July 26 2006 Midterm

# July 26 2006 Midterm - (measured in hours is given by f x =...

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STAT 116 STAT 116 Midterm July 26, 2006 9:00 am - 10:00 am Please show all work. The total score is 100. There are 6 problems and each problem is worth 16 points. There are 4 free points. Name: 1

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1. Three bags lie on the table. One has two gold coins, one has two silver coins, and one has one silver and one gold. You pick a bag at random, and pick out one coin from it. If this coin is gold, what is the probability you picked from the bag with two gold coins? 2
2. Suppose that the number of accidents occuring on a highway each day is a Poisson random variable with λ = 3 . Find the probability that 3 or more accidents occur today. 3

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3. The probability density function of X , the lifetime of a certain type of electronic device

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Unformatted text preview: (measured in hours) is given by f ( x ) = ( 10 x 2 , for x > 10 , for x ≤ 10 . (a) Find P ( X > 20) . (b) What is the cumulative distribution function of X ? 4 4. Suppose we put 10 indistinguishable balls into 6 boxes. What is the probability there will be exactly 2 empty boxes? 5 5. When Al and Bob play tennis, Al wins a set with probability . 7 while Bob wins with probability . 3 . What is the probability Al will be the ﬁrst to win 2 sets? 6 6. What is the probability that 5 people have birthdays that fall in two months but not all in the same month? (Assume that a birthday is equally likely to fall in any of the 12 months.) 7...
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## This note was uploaded on 11/15/2008 for the course STATS 116 taught by Professor Staff during the Summer '07 term at Stanford.

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July 26 2006 Midterm - (measured in hours is given by f x =...

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