Consider writing on to a computer disk and then sending it through a certifier t

Question

Consider writing on to 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 variance 0.3.

What is the probability that a disk has exactly one missing pulse?

What is the probability that a disk has at least two missing pulses?

If 5 disks are selected at random, what is the chance that exactly 4 of them have no missing pulses?

Suppose disks are selected and tested one by one to find the first disk with at least one missing pulse. What is the probability that the first disk with at least one missing pulse will be found in the 8th draw?

Explanation / Answer

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 ^-0.3 * 0.3^1 / 1! = 0.2222

b.

P( X < 2) = P(X=1) + P(X=0)
= e^-0.3 * 1 ^ 1 / 1! + e^-0.3 * ^ 0 / 0!   
= 0.9631

P( X > = 2 ) = 1 - P (X < 2) = 0.0369

c.
When 5 disks are selected at random, rate is = 5 * 0.3 = 1.5
P( X = 4 ) = e ^-1.5 * 1.5^4 / 4! = 0.0471

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