A USB flash drive is sometimes used to backup computer files

A USB flash drive is sometimes used to backup computer files. However, in the past, a less reliable backup system that was used was a computer tape, and flaws occurred on these tapes. In a particular situation, flaws on a used computer tape occurred on the average of one flaw per 1200 feet. If one assumes a Poisson distribution, what is the distribution of X, the number of flaws in a 4800 foot roll? What is the probability mass function of X and find P(x=0) and P(x<=3).

Solution

X follows Poisson distribution with mean=4

So the probability mass function of X is

P(X=x)=(4^x)*exp(-4)/x! for x=0,1,2,...

So P(x=0) =(4^0)*exp(-4)/1=0.01831564

P(x<=3) = P(X=0)+P(X=1)+P(X=2)+P(X=3)

=(4^0)*exp(-4)/1+...+(4^3)*exp(-4)/3!

=0.4334701