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?
Accepted Solution
A:
Answer: The mean number of checks written per day [tex]=0.3452[/tex]Standard deviation[tex]=0.5875[/tex]Variance [tex]=0.3452[/tex]Step-by-step explanation:Given : The total number of checks wrote by person in a year = 126Assume 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 :-[tex]\lambda=\dfrac{126}{365}\approx0.3452[/tex]Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. [tex]\sigma^2=\lambda=0.3452[/tex]Standard deviation : [tex]\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875[/tex]