Question

Last​ year, a person wrote 126 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  $=0.3452$

Standard deviation$=0.5875$

Variance  $=0.3452$

Step-by-step explanation:

Given : The total number of checks wrote by person in a year = 126

Assume that the year is not a leap year.

Then  1 year = 365 days

Let the random variable x represent the number of checks he wrote in one​ day.

Then , the mean number of checks wrote by person each days id=s given by :-

$\lambda=\dfrac{126}{365}\approx0.3452$

Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. $\sigma^2=\lambda=0.3452$

Standard deviation : $\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875$