University of California, Los Angeles
Department of Statistics
Statistics 100A
Instructor: Nicolas Christou
Exam 2  Practice problems
Problem 1
Answer the following questions:
a. The amount of snow during winter at a certain mountain in California follows the normal distribution with mean
μ
= 50
inches and standard deviation
σ
= 5 inches. Find the probability that this year’s amount of snow at at this location will
be between 43.85 and 56.75 inches.
b. Refer to question (a). What is the distribution of the amount of snow in centimeters? Note: 1 inch=2.54 cm.
c. Let
X
1
,X
2
,
···
,X
n
be independent gamma random variables with
X
i
∼
Γ(
α
i
,β
) (same
β
but diﬀerent
α
). What is the
distribution of
X
1
,
+
X
2
+
···
+
X
n
?
Hint
: Use moment generating functions.
d. Let
X
∼
Γ(3
,
1). Find
E
(
X
4
).
Problem 2
The number of internet users that visit a particular website follows the Poisson distribution with
λ
= 120 per hour (2 per
minute).
a. Let
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 Fall '07
 Wu
 Statistics, Normal Distribution, Probability theory, probability density function, Weibull, Weibull distribution

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