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 ? = .2. (Suggested in “Average Sample Number for Semi-Curtailed Sampling Using the Poisson Distribution,” J. Quality Technology, 1983: 126–129.) a.? hat is the probability that a disk has exactly one missing pulse? b.?? hat 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 : Step 1 : Here X is the number of missing pulses when data from a computer disk sending through a certifier which counts missing pulses. It is also given that X~poisson distribution with mean or parameter = 0.2. We have to find probabilities for different values of X. Step 2 : a) We have to find the probability that a disk has exactly one missing pulse. X~poisson distribution, the probability mass function of X e x P(x) = , x= 0,1,2,3,.. .here = 0.2. x! So the probability that a disk has exactly one missing pulse e 0.20.2 1 P(X=1) = 1! = 0.164 b) We have to find the probability that the disk has at least two missing pulses. P(X2)= 1-P(X<2) = 1-(P(X=0)+P(X=1)) 0.2 0 P(X=0) = e 0.2 0! = 0.8187 P(X 2) = 1 ( 0.164 + 0.8187) = 1- (0.9827) = 0.0173