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Homework Assignment 15:
(1) The random variable S follows a binomial distribution with n = 3 and p = 1/3. The following procedure
simulates S:
Generate a uniform random number U on [0,1] and let
0, if
U
≤
a
S =
1, if
a
< U
≤
b
2, if
b
< U
≤
c
3, if
c
< U
Determine
a
+
b
+
c
. (Ans 2)
(2) Mike is practicing his simulation skills.
He generates 1000 values of the random variable
X
as follows:
(i)
He generates the observed value
λ
from the gamma distribution with
α
= 2 and
β
= 1 (hence
with mean 2 and variance 2).
(ii)
He then generates
x
from the Poisson distribution with mean
.
(iii)
He repeats the process 999 more times: first generating a value
, then generating
x
from the
Poisson distribution with mean
.
(iv)
The repetitions are mutually independent.
Calculate the expected number of times that his simulated value of
X
is 3. (Ans 125)
(3) Insurance for a city’s snow removal costs covers four winter months.
There is a deductible of
10,000 per month.
The insurer assumes that the city’s monthly costs are independent and
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 Spring '11
 CharlesDann

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