2. Suppose that the magnitude of earthquakes striking a region has a gamma distr

Question

2. Suppose that the magnitude of earthquakes striking a region has a gamma distribution with = 0.8 and = 2.4.

(a) What is the mean magnitude of earthquakes striking the region?

(b) What is the probability that the magnitude an earthquake striking the region will exceed 3.0 on the Richter scale?

(c) What is the probability that an earthquake striking the regions will fall between 2.0 and 3.0 on the Richter scale?

(d) Compare these answers to question 1.For example,which probabilities are larger? Explain.

Explanation / Answer

a) for gamma distribution mean magnitude of earthquakes = =0.8*2.4=1.92

b)

probability that the magnitude an earthquake striking the region will exceed 3.0 on =P(X>3) =1-P(X<3)

=1-0.7869 =0.2131

c)

probability that an earthquake striking the regions will fall between 2.0 and 3.0 on the Richter scale

=P(2<X<3) =0.7869-0.6602 =0.1267

d) please provide detail of question 1

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