introduction to stats

Question

n a Poisson distribution, μ = 0.34. (Round the final answers to 4 decimal places.) 

 

a. What is the probability that x = 0?

 

Probability          ?

 

b. What is the probability that x > 0?

 

Probability          ?

Answer 1

If the random variable X has a Poison distribution then its mean µ = λ the parameter of a Poisson distribution. a) For a Poisson distribution the probability Pr(X=n) = ( e^–λ λⁿ) / n! (Note n! = 1*2*3 ...*n and 0! = 1)

In this problem μ = λ = 0.34

So the probability Pr(X = 0) = (e^-0.34_* 0.34⁰) / 0! = e^-0.34 = 0.71177

b) Pr(X > 0) = 1 - Pr(X = 0) - 1 - 0.71177 = 0.28823