Answer:
a) P(1) = 0.1637
b) [tex]P(x\geq 2) = 0.0176[/tex]
c) E(x) = 0.2
Step-by-step explanation:
If X follows a poisson distribution, the probability that a disk has exactly x missing pulses is:
[tex]P(x)=\frac{e^{-m}*m^x}{x!}[/tex]
Where m is the mean and it is equal to the value of lambda. So, replacing the value of m by 0.2, we get that the probability that a disk has exactly one missing pulse is equal to:
[tex]P(1)=\frac{e^{-0.2}*0.2^1}{1!}=0.1637[/tex]
Additionally, the probability that a disk has at least two missing pulses can be calculated as:
[tex]P(x\geq 2)=1-P(x<2)[/tex]
Where [tex]P(x<2)=P(0)+P(1)[/tex].
Then, [tex]P(0)[/tex] and [tex]P(x\geq 2)[/tex] are calculated as:
[tex]P(0)=\frac{e^{-0.2}*0.2^0}{0!}=0.8187\\P(x\geq 2) = 1 - (0.8187 + 0.1637)\\P(x\geq 2) = 0.0176[/tex]
Finally, In the poisson distribution, E(x) is equal to lambda. So E(x) = 0.2
