University of California, Los Angeles
Department of Statistics
Statistics 100A
Instructor: Nicolas Christou
Exam 2
13 May 2011
Name:
Problem 1
(25 points)
Answer the following questions:
a. Let
X
∼
Γ(
α, β
). Show that
Y
=
cX
follows Γ(
α, cβ
).
b. Let
X
∼
N
(
μ, σ
). Find the distribution of
Y
=
e
X
.
c. Suppose the radius of a circle
X
is a random variable that follows the exponential distribution with parameter
λ
. Find
the distribution of the area of the circle:
Y
=
πX
2
.
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Problem 2
(25 points)
In California earthquakes of magnitude 12 in the Richter scale are recorded at the rate of 8 per hour according to a Poisson
distribution. Answer the following questions:
a. What is the probability that more than 12 earthquakes (of magnitude 12 in the Richter scale) will be recorded in the
next hour. Please write the expression that computes the exact probability (no computations).
b. Approximate the probability of part (a) using the normal distribution.
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 Fall '09
 Wu
 Normal Distribution, Variance, Probability theory, probability density function, following questions, Richter scale

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