SIEO 3600 (IEOR Majors)
Assignment #9
Introduction to Probability and Statistics
March 30, 2010
Assignment #9
– due April 6th, 2010
(
Uniform, Exponential and Normal random variables
)
1. If
X
is a normal random variable with parameters
μ
= 10,
σ
2
= 26, compute
(a)
P
(
X >
5);
(b)
P
(4
< X <
16);
(c)
P
(
X <
8);
(d)
P
(
X <
20);
(e)
P
(
X >
16).
Hint:
express these probabilities in terms of the standard normal CDF function Φ and use
the tables at the back of the textbook.
2. The annual rainfall (in inches) in a certain region is normally distributed with
μ
= 40,
σ
= 4.
What is the probability that in 2 of the next 4 years the rainfall will exceed 50 inches? Assume
that the rainfalls in diﬀerent years are independent.
3. A random variable
X
is said to have a
lognormal
distribution if
Z
≡
log
X
is normally
distributed. If
X
is lognormal with
E
[
Z
] =
μ
and var(
Z
) =
σ
2
, then
(a) determine the probability distribution function (PDF) of
X
.
(b) What is
P
(
X
≤
x
)?
4. In the midterm of a probability course, the scores that students get follow a
uniform
distri
bution from 20 to 100. Due to popular grieving, the professor decides to rescale the results.
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 Spring '10
 YUNANLIU
 Normal Distribution, Standard Deviation, Probability distribution, Probability theory, CDF

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