Last year a man wrote 142 checks. Let random variable x represent the number of...

stop2dance3l

stop2dance3l

Answered

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?

Answer & Explanation

Durst37

Durst37

Expert

2022-01-16Added 37 answers

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) λ=0.389041
X Poisson (λ=0.389041)
Mean of poisson random variable is equal to its rate parameter λ
Mean or expected value, E(X)=μ=0.3890
Variance of process is equal to its rate parameter λ
Variance, V(X)=σ2=0.3890
Standard deviation of poisson random variable is equal to square root of its rate parameter λ i.e x=0.389041=0.623732
Standard deviation, σ=0.6237
Debbie Moore

Debbie Moore

Expert

2022-01-17Added 43 answers

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 λ=0.3890(=142365).
The mean is,
μ=λ
=0.389
The mean number of checks written per day is 0.389.
The variance is obtained as shown below:
The variance is,
σ2=λ
=0.389
The variance is 0.389.
The standard deviation is obtained as shown below:
The standard deviation is,
σ=x
=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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