Question

# Suppose that the number of spam emails that Alex receives has a Poisson distribution with µ...

Suppose that the number of spam emails that Alex receives has a Poisson distribution with µ = 2.3 per day. What is the probability that the number of spam emails Alex receives in a day is within one standard deviation of the mean? Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.

Given data

Mean = = 2.3

Standard deviation =

= 1.52

= Mean - Standard deviation

= 2.3 - 1.52

= 0.78

= Mean + Standard deviation

= 2.3 + 1.52

= 3.82

= 0.699

Poisson Distribution

P( k events in interval )

where

• is the average number of events per interval.
• e is the number 2.71828 ....(Euler's number ) the base of the natural logarithms
• k takes values 0,1,2,.....
• k! = k * (k-1) * ( k - 2) * -------- * 2 * 1 is the factorial of k.

This equation is the probability mass function (PMF) for a Poission distribution.

 x P(X = -x) 0 0.10026 1 0.2306 2 0.26518 3 0.20331

Hence

= 0.699

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