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December 2, 2010
Math 351  Test 3
1. An urn has two black and one white ball. An experiment consists of taking two balls from
the urn. Call it “success” if both of them are black and call it “failure” if they are not both
black. After you have chosen the two balls, put them back in the urn and then repeat. Let
X
be the number of trials to the ﬁrst success and let
Y
be the the number trials to the ﬁfth
success.
(a) Calculate
p
, the probability of success on any one trial.
(b) What kind of random variable is
X
? What kind of random variable is
Y
?
(c) What is the expected value of
X
?
(d) What is
P
{
Y
= 10
}
?
2. Consider a horizontal line segment of total length 15 inches. Fix a point
P
along the line
segment at a distance 3 from the right side. Let
X
be a randomly chosen point along the line
segment such that
X
is uniformly distributed. Let
Y
be the distance from
X
to
P
if
X
is to
the right of
P
and let
Y
be 12 if
X
is to the left of
P
. Write down the expression (in terms
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 Spring '08
 Moumen,F
 Math, Probability

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