stop2dance3l

2022-01-16

Last year a man wrote 142 checks. Let random variable x represent the number of checks he wrote in a day, and assume it has a Poisson distribution. What is the mean number of checks written per day?

Durst37

Expert

Let X be the number of checks in 1 days
The rate of 142 checks in 365 days is same as 142/365 * 1=0.389041 in 1 days
X follows Poisson distribution with parameter (rate) $\lambda =0.389041$
X $\sim$ Poisson ($\lambda =0.389041$)
Mean of poisson random variable is equal to its rate parameter $\lambda$
Mean or expected value, $E\left(X\right)=\mu =0.3890$
Variance of process is equal to its rate parameter $\lambda$
Variance, $V\left(X\right)={\sigma }^{2}=0.3890$
Standard deviation of poisson random variable is equal to square root of its rate parameter $\lambda$ i.e $\sqrt{x}=\sqrt{0.389041}=0.623732$
Standard deviation, $\sigma =0.6237$

Debbie Moore

Expert

The mean number of checks written per day is obtained as shown below:
Let x denotes the number of checks written per day.
From the information given, last year a person wrote 142 checks which means $\lambda =0.3890\left(=\frac{142}{365}\right)$.
The mean is,
$\mu =\lambda$
=0.389
The mean number of checks written per day is 0.389.
The variance is obtained as shown below:
The variance is,
${\sigma }^{2}=\lambda$
=0.389
The variance is 0.389.
The standard deviation is obtained as shown below:
The standard deviation is,
$\sigma =\sqrt{x}$
$=\sqrt{0.389}$
=0.624
The standard deviation is 0.624.
The mean number of checks written per day is 0.389.
The variance is 0.389.
The standard deviation is 0.624.

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