IEOR 4701
Assignment 1
Summer 2011
1. Ross, 4.28
A sample of 3 items is selected at random from a box containing 20 items of which 4 are
defective. Find the expected number of defective items in the sample.
2. Ross, 4.41
A man claims to have extrasensory perception. As a test, a fair coin is ﬂipped 10 times, and
the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the
probability that he would have done at least this well if he had no ESP?
3. Ross, Theoretical 4.28.
Let
X
be a negative binomial random variable with parameters
r
and
p
, and let
Y
be a
binomial random variable with parameters
n
and
p
. Show that
P
{
X > n
}
=
P
{
Y < r
}
by means of probabilistic interpretation of these random variables. Do
not
attempt to give
any analytical proof of the preceding.
4. At 8:59 AM, A, B, C are waiting (in that order) outside a bank that will open at 9 AM. The
bank has two tellers; each of the requirements that A, B, and C are bringing to the bank are
i.i.d. exponentially distributed random variables with mean 1. What is the probability that
A is the last one to leave the bank?
5. Ross, Theoretical 4.20
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 Summer '10
 KarlSigma
 Probability theory, binomial random variable, Poisson random variable

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