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

2 Answers
Narad T.
Jan 13, 2017

The answer is =0.8009

Explanation:

The Poisson distribution is

P(x)=(e^-mu mu^x)/(x!)

mu=3

3! =3*2*1

P(x>=2)=1-P(1)-P(0)

P(1)=(e^-3 *3^1)/(1!)=3/e^3

P(0)=e^-3=1/e^3

Therefore,

P(x>=2)=1-P(1)-P(0)=1-0.0498-0.1494=0.8009

Shwetank Mauria
Jan 13, 2017

P(x>=2)=0.800852

Explanation:

In a Poisson probability distribution, if mean value of success is mu,

the probability of getting x successes is given by

P(x)=(e^(-mu)mu^x)/(x!)

Now P(x>=2) means 1-P(x=0)-P(x=1)

Here mu=3 and e^(-mu)=e^(-3)=0.049787

and hence, desired probability is

1-(e^(-3)3^0)/(0!)-(e^(-3)3^1)/(1!)

= 1-e^(-3)xx(1+3)

= 1-0.049787xx4

= 1-0.199148

= 0.800852

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