Answer:
a) 0.222
b)0.037
c)0.549
Step-by-step explanation:
Let's start defining the random variable ⇒
X : ''The number of missing pulses''
X can be modeled as a Poisson random variable.
X ~ Po(λ)
In a Poisson distribution : μ = λ
Where μ is the mean of the variable.
X ~ Po(0.3)
The probability function for a Poisson random variable is :
In the equation I replace λ = m

Where P(X=x) is the probability of the random variable X to assume the value x
e is the euler number
m = λ is the mean of the variable
In this exercise :

is the probability function.
For a)

For b)

![P(X\geq 2)=1-[P(X=0)+P(X=1)]](https://tex.z-dn.net/?f=P%28X%5Cgeq%202%29%3D1-%5BP%28X%3D0%29%2BP%28X%3D1%29%5D)

c)
Let's define A :''a disk doesn't contain a missing pulse''
We are looking for P(A1∩A2) of two different disk don't have a missing pulse.
Because of the independence we can write this probability as
P(A1∩A2)= P(A1).P(A2)
The probability of a random disk to don't have a missing pulse is P(X=0)
⇒
![P(A1).P(A2)=[P(X=0)].[P(X=0)]](https://tex.z-dn.net/?f=P%28A1%29.P%28A2%29%3D%5BP%28X%3D0%29%5D.%5BP%28X%3D0%29%5D)
![[P(X=0)].[P(X=0)]=(e^{-0.3})(e^{-0.3})=0.549](https://tex.z-dn.net/?f=%5BP%28X%3D0%29%5D.%5BP%28X%3D0%29%5D%3D%28e%5E%7B-0.3%7D%29%28e%5E%7B-0.3%7D%29%3D0.549)