Question

Last​ year, a person wrote 128 checks. Let the random variable x represent the number of checks he wrote in one​ day, and assume that it has a Poisson distribution. What is the mean number of checks written per​ day? What is the standard​ deviation? What is the​ variance?

Answer 1

Answer: The mean number of checks written per​ day =
`\lambda=0.3507`

`\text{Variance}(\sigma^2)=\lambda=0.3507`

`\text{Standard deviation}=0.5922`

Explanation:

Given : A person wrote 128 checks in last year.

Consider , the last year is a no-leap year.

The number of days in ;last year = 365 days

Let X be the number of checks in one day.

Then ,
`X=(128)/(365)=0.350684931507\approx0.3507`

The mean number of checks written per​ day =
`\lambda=0.3507`

Now X follows Poisson distribution with parameter
`\lambda=0.3507`.

Then ,
`\text{Variance}(\sigma^2)=\lambda=0.3507`

`\Rightarrow\sigma=√(\lambda)=√(0.3507)=0.59219929078\approx0.5922`