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?

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Durst37 · Accepted Answer

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 · Accepted Answer

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.

Last year a man wrote 142 checks. Let random variable

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