Question

In: Statistics and Probability

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find...

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find the maximum usual value for x.
Round your answer to two decimal places.

2.

In one town, the number of burglaries in a week has a Poisson distribution with mean μ = 7.2. Let variable x denote the number of burglaries in this town in a randomly selected month. Find the smallest usual value for x. Round your answer to three decimal places.

(HINT: Assume a month to be exactly 4 weeks)

Expert Solution

Solution:

Question 1) Given: the random variable x has a Poisson Distribution with mean μ = 53.4.

For Poisson distribution: Mean = Variance = μ = 53.4.

Standard Deviation of Poisson distribution is:

We have to find the maximum usual value for x.

Maximum usual value for x =

Maximum usual value for x =

Question 2)

Given: the number of burglaries in a week has a Poisson distribution with mean μ = 7.2.

x = the number of burglaries in this town in a randomly selected month.

Since mean is given for a week and x is defined per month, so we need to find mean number of burglaries in a month.

For a month number of weeks = 4

Thus new mean = 4 * μ = 4 * 7.2 = 28.80

and

Thus

The smallest usual value for x =

The smallest usual value for x =

orchestra answered 1 year ago

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