Which numbers make a true statement when placed in the box?
1 answer:
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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)
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)
⇒