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 = 0.7. (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?

You may need to use the appropriate table in the Appendix of Tables to answer this question.

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
vehicles passing the mile marker every 15 minutes is 48.7
=48.7
a)
USED AN EXCCEL FORMULA : ROUND(POISSON(50,48.7,TRUE),4)
P (X < 50) = 0.555
P( X > = 50 ) = 1 - P (X < 50) = 0.445

b)
For 15 mins s.d = Sqrt() = Sqrt(48.7)= 6.9785
For 30 mins s.d = Sqrt() = Sqrt(48.7*2)= 9.8691

c)
USED AN EXCCEL FORMULA : ROUND(POISSON(100,97.4,TRUE),4)
P (X < 100) = 0.5905
P( X > = 100 ) = 1 - P (X < 100) = 0.4095

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 ^-0.7 * 0.7^1 / 1! = 0.3476

b)
P( X < 2) = P(X=1) + P(X=0)
= e^-0.7 * 1 ^ 1 / 1! + e^-0.7 * ^ 0 / 0!
= 0.8442
P( X > = 2 ) = 1 - P (X < 2) = 0.1558

c)
For 2 disks , Mean = 2*0.7 = 1.4
P( X = 0 ) = e ^-1.4 * 1.4^0 / 0! = 0.2466