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exam2_100a_s11

# exam2_100a_s11 - University of California Los Angeles...

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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 1-2 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 1-2 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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