Consider a Poisson distribution with μ=3. What is P(x≥2)?

idiopatia0f

idiopatia0f

Answered

2022-01-16

Consider a Poisson distribution with μ=3. What is P(x2)?

Answer & Explanation

Archie Jones

Archie Jones

Expert

2022-01-16Added 34 answers

Explanation:
The Poisson distribution is
P(x)=eμμxx!
μ=3
3! = 3*2*1
P(x2)=1P(1)P(0)
P(1)=e3311!=3e3
P(0)=e3=1e3
Therefore,
P(x2)=1P(1)P(0)=10.04980.1494=0.8009
Explanation:
In a Poisson probability distribution, if mean value of success is μ,
the probability of getting x successes is given by
P(x)=eμμxx!
Now P(x2) means 1-P(x=0)-P(x=1)
Here μ=3 and eμ=e3=0.049787
and hence, desired probability is
1e3300!e3311!
=1e3×(1+3)
=10.049787×4
=1-0.199148
=0.800852
peterpan7117i

peterpan7117i

Expert

2022-01-17Added 39 answers

Compute P(X2)
The required probability is
P(X2)=1P(X<2)
=1-[P(X=0)+P(X=1)]
=1-[0.049787+0.149361] from statistical table
=0.8009
The required P(X2)=0.8009

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