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Unformatted text preview: STAT 116 STANFORD UNIVERSITY Department of Statistics MIDTERM EXAMINATION
STATISTICS 116 Instructor: Professor Anthony D’Aristotile July 23, 2007
9:00 am  10:00 am IMPORTANT: Please, show all your work and justify your assertions. However,
you may leave your answers in indicated form. There are 100 total points. STUDENT ' Name:
STUDENT ID : 1. (20 points)
A drawer contains 10 black, 8 brown, and 6 blue socks. If we pick two socks at random,
what is the probability they match? 2. (20) If 6 balls are thrown at random into 10 boxes, what is the probability no box will contain
more than 1 ball? 3. (7 + 13)
Supppose X is exponentially distributed with parameter A = 3. (3) Find P[X 211)
(b) Find the probability density function of Z = X2 4. (20)
On a ﬂight from Urbana, Illinois to Paris my luggage did not arrive with me. It had been
transferred three times and the probabilities that the transfer was not done in time were
estimated to be in the order of transfer. What is the probability that the ﬁrst airline
goofed? U1 5. (10 + 10)
Each of n boys and 11 girls, independently and randomly chooses a member of the other sex.
If a boy and girl choose each other, they become a couple. Number the girls, and let G: be
the event that girl number i is part of a couple. (a) What is P[Gi)?
(b) Ift',j are distinct positive integers between 1 and it, what is 33031ij .335 u... qunmmqm vambmFﬂbﬁqamsaz
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 Summer '07
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 Probability

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