Consider writing onto a computer disk and then sending it th

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter mu = 0.8. (Round your answers to three decimal places.) (a) What is the probability that a disk has exactly one missing pulse? (b) What is the probability that a disk has at least two missing pulses? (c) If two disks are independently selected, what is the probability that neither contains a missing pulse?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X = 1 ) = e ^-0.8 * 0.8^1 / 1! = 0.359
b)
P( X < 2) = P(X=1) + P(X=0) +
= e^-0.8 * 1 ^ 1 / 1! + e^-0.8 * ^ 0 / 0! +   
= 0.809
P( X > = 2 ) = 1 - P (X < 2) = 0.191
c)
P( X = 0 ) = e ^-0.8 * 0.8^0 / 0! = 0.449