Question

2. In the month of April the average number of tornadoes per week in Oklahoma has historically been 3.5.

(a) What is the probabilty there are at least 3 tornadoes in a random week (in April)?

(b) What is the expected number of tornadoes in the entire month? You can pretend that there are exactly four weeks in April. What is the variance?

(c) What is the probability that it takes 3 days before a tornado occurs?

(d) What is the expected amount of time before a tornado occurs?

(e) Suppose we took a random sample of 5 different weeks from past Aprils and counted the number of tornados in each. Use the method of moments to create an estimator for k.

Answer 1

a)

Mean/Expected number of events of interest:   λ =

3.5

poisson probability distribution

P(X=x) = e-λλx/x!

X	P(X)
0	0.0302
1	0.1057
2	0.1850

p(x>=3) = 1-(p(0)+p(1)+p(2))

=0.3208

.

b)

mean=3.5*4 =14

variance = λ   14

c)

For Day

Mean/Expected number of events of interest: λ =                0.5

X	P(X)
0	0.6065

Probability = 0.6065 * 0.6065 * 0.6065 * (1-0.6065)

= 0.5542

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