CS206
HW5
Nov 6, 2009
(* due in class Nov 25, or before, at my office)
(** is more challenging. You do not need to hand it in)
1. Do question 10 from HW4,
now
using the negative binomial random variable.
2. A fair die is tossed twice. Let
Z
be the sum of the tosses and
W
be the difference. Are
Z
and
W
independent? Explain.
3. (*) Find
V
(
Z
) in the above problem.
4. (*) Find the expected number of people getting their own hats in the 4 hat experiment. (Do
this using (i)
E
(
X
) =
∑
w
∈
S
X
(
w
)
P
(
w
) and (ii)
E
(
X
) =
∑
a
i
∈
Range
(
X
)
a
i
f
X
(
a
i
).)
5. (*) Let
X
be the number of people who get their own hat in the 4 hat experiment.
Find
V
(
X
), the variance.
6. (**) As above, but with the
n
hat experiment.
7. Similar to the question in the midterm, a student takes CS111, CS112, CS113, CS205, CS206,
CS344, and in each receives a grade of
F, D, C, C
+
, B, B
+
, A
. The grade is given at random.
Let
N
be the random variable that counts the number of
distinct (i.e. different)
grades he
receives. Compute
E
(
N
) using the method of indicators.
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 Spring '08
 Fredman
 Variance, Probability theory, hat experiment

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