You may need to use t Noed Help? Hasd ok is Tder Notes Ask Your 5 13 points Cons

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You may need to use t Noed Help? Hasd ok is Tder Notes Ask Your 5 13 points 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 -03. (Round your answers to three decimal places.) (a) What is the probablity 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? 0/ You may need to use the appropriate table in the Appendix of Tables to answer this question 0/2 Submit Assignment Save Assignment Progress 8 4 Q W s lock

Explanation / Answer

pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.   
x = is the number of independent trials
I.
mean =
= 0.3
A.
P( X = 1 ) = e ^-0.3 * 0.3^1 / 1! = 0.22225
B.
P( X < 2) = P(X=1) + P(X=0)   
= e^-0.3 * 1 ^ 1 / 1! + e^-0.3 * ^ 0 / 0!   
= 0.96306,
P( X > = 2 ) = 1 - P (X < 2) = 0.03694
C.
the probability of choosing a missing pulse ,
P( X = 0 ) = e ^-0.3 * 0.3^0 / 0! = 0.74082

& now, 2 disks are independently selected
X ~ B(2, 0.4082)

P( X = 0 ) = ( 2 0 ) * ( 0.74082^0) * ( 1 - 0.74082 )^2
= 0.0672

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