# 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?

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?
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Savanna Smith
pmf of P.D is $=f\left(k\right)=e-\lambda \frac{\lambda x}{x}$!where$\lambda$ = parameter of the distribution. x = is the number of independent trials
I.
mean = $\lambda$
= 0.3
A.
$P\left(X=1\right)={e}^{-0.3}\cdot {0.3}^{1/1!}=0.22225$
B.
$P\left(X<2\right)=P\left(X=1\right)+P\left(X=0\right)={e}^{-0.3}\cdot {1}^{1/1!}+{e}^{-0.3}{\cdot }^{0/0!}=0.96306,$
$P\left(X>=2\right)=1-P\left(X<2\right)=0.03694$
C.
the probability of choosing a missing pulse ,
$P\left(X=0\right)={e}^{-0.3}\cdot {0.3}^{0/0!}=0.74082$
now, 2 disks are independently selected
$X\sim B\left(2,0.4082\right)$
$P\left(X=0\right)=\left(20\right)\cdot \left({0.74082}^{0}\right)\cdot \left(1-0.74082{\right)}^{2}$
$=0.0672$