IE 300 / GE 331 Spring 2009
Homework #4
Due: Mar. 19th
Problem 1.
A particular professor is known for his arbitrary grading policies. Each
paper receives a grade from the set
{
A, A

, B
+
, B, B

, C
+
}
, with equal probability,
independent of other papers. How many papers do you expect to hand in before you
receive each possible grade at least once?
Problem 2.
Calamity Jane goes to the bank to make a withdrawal, and is equally
likely to find 0 or 1 customers ahead of her. The service time of the customer ahead,
if present, is exponentially distributed with parameter
λ
. What is the CDF of Jane’s
waiting time?
Problem 3.
Alvin throws darts at a circular target of radius
r
and is equally likely
to hit any point in the target. Let
X
be the distance of Alvin’s hit from the center.
(a) Find the PDF, the mean, and the variance of
X
.
(b) The target has an inner circle of radius
t
.
If
X
≤
t
, Alvin gets a score of
S
= 1
/X
. Otherwise his score is
S
= 0. Find the CDF of
S
. Is
S
a continuous
random variable?
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 Spring '09
 NegarKayavash
 Probability theory, Alvin, Calamity Jane, marginal pdf

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