Question

Can you check my answers and solve problem f and g

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Oklahoma is not historically known for experiencing earthquakes. Up until 2008, Oklahoma experienced a constant rate of about 1.5 perceptible earthquakes per year on average.

a) Assuming that earthquakes are random and independent, with a constant rate of 1.5 per year, he count of perceptible earthquakes per year in Oklahoma should have a Poisson distribution with mean 1.5. What is the standard deviation of the number of earthquakes per year?

Answer: 1.255

b) Making the same assumptions as in part (a), use one or two R functions to compute the probability of seeing less than two earthquakes per year.

Answer: ppois(1,1.5)

0.5578254

c) Do the same calculation as above, this time using only a hand calculator. Show your work and round your final percentage to two decimal places.

Answer: 0.5578

d) In 2013, Oklahoma experienced 109 perceptible earthquakes (an average of two per week). Assuming the same model as above, write an equation to show how the chance of experience 109 earthquakes or more can be written as a function of the probability at or below some k.

Answer: P(k>=109) = 1 - P(k<109) where k= 0,1,2,.....108

e) Use R, calculate the probability of observing 109 perceptible earthquakes or more. Write a sentence describing the chance of seeing such an event assuming the specified Poisson distribution (i.e., is it rare or common?)

Answer: dpois(109,1.5)

2.415353e-158

f) Based on your answer in question (e), would you conclude that the mean number of perceptible earthquakes has increased? Why or why not?

g) Would knowing that the number of perceptible earthquakes was 585 in 2014 support your conclusion?

Answer 1

The number of perceptible earthquake has Poisson distribution.

Poisson PMF is

a) The mean and variance of the Poisson distribution is . The standard deviation is

b) The probability,

> ppois(1,1.5)
[1] 0.5578254

c) Using hand calculator

d) The equation to show how the chance of experience 109 earthquakes or more can be written as a function of the probability at or below some is (use complementary probability)

e) The probability of observing 109 perceptible earthquakes or more is

> 1-ppois(108,1.5)
[1] 0

It is very rare since the probability is 0.

f) From part (d), the number of Earthquakes has increased from 1.5 year to 2 per week.

g) Yes.