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Unformatted text preview: Math 351 Exam 1
W. T. Kiley October 13, 2006 Clearly show your work and answers in the space provided. It is not
necessary to do the arithmetic. Follow the Honor Code. 1. You draw 2 different cards frOm a deck. Are the events:
first is a heart; second is a 'heart (Z) 2. For the above experiment, find the probabilities that:
a) both are hearts; b) at least one is a heart. a) Wag): P/AWKB/A) ; $5.5, 3. You choose 4 people from a group of 5 women and 5 men. Find the probability
that exactly half are women if chosen: a) with replacement; b) without eace. MWMWELM:¢W was)“ .5)
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m M x 4. The probability density function for X with state space [0.40) is e . Find:
a) cumulative distribution function ; b) expected value. w» z Lu W Efﬂ’rjj; _[ "A : jmie‘z ¢: ‘jvx l”: 9 [745) 5. 5% of a population are liars. 90% of the liars fail a lie detector test and 20% of nonliars fail. Find the probabilities that a person:
a) fails the test; b) is a liar, given that he fails the test. a.) P/F) = P/F/IL) + My; If) “a” 537* . €522. : 2 Pat/L F/L)‘ .0534 : (35>j> 6. X is uniform on [2,3]. Find the probabilities that:
a) —1 < X, given that X < 1; b) x < 1, given that —1 < x. a) PFI<><J><<I> ; P(—I<x~’/)/p(»,2<x<c E?) >= ,0 P(/< X [44%) ‘ P(~/< X<I)/}>{—/<Xz3) 11:35 [ £5?) 7. The p.m.f. of (X,Y) is q(1,3) = .2, q(1,4) = .1, q(2,3) .3, q(2,4) Find a)the marginal p.m.f. of X; b) the expected value of X. ‘ 8. For a Poisson process with on average 0.2 successes per minute, find the
probabilities that: a) there is at least one success in the first 5 minutes 2. 2'7=/7
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b) the time until the first succesﬁ7is at most 5 minutes. (73
PM; =47]: 2""’62'$> A! =17,” 1 00 Pin/€22] 2 / W503 =
1A Pﬁissk PIA/W] = .4. o
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 Spring '08
 Moumen,F
 Probability theory, probability density function, Cumulative distribution function, lie detector test

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