Consider writing a computer disk and then sending it throught a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter mu=0.3 a) What is the probability that a disk has exacly 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?

Owen Mathis 2022-11-03 Answered
Consider writing a computer disk and then sending it throught a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter μ = 0.3
a) What is the probability that a disk has exacly 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?
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Answers (1)

Savanna Smith
Answered 2022-11-04 Author has 17 answers
pmf of P.D is = f ( k ) = e λ λ x x !where λ = parameter of the distribution. x = is the number of independent trials
I.
mean = λ
= 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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