Poisson Distribution

Question

Using a Poisson Distribution, find P(3) if μ = 2. Round to 3 decimal places if necessary.

Answer 1

As a reminder, the Poisson distribution is µ^ke^-µ/k!

 

To find P(3), simply plug in 3 for k and 2 for µ.  This is telling you the probability that k is exactly three if the mean of the Poisson distribution is 2.

 

2³e^-2/3! is what you plug into the calculator, which is approximately 0.180.

 

Hope this helps!

 

Oliver S

 

 

Answer 2

P(x;μ) = (e^-μ)(μ^x) / x!

P(3;2) = (e^-2)(2³) / 3!

P(3;2) ≈ (0.135335283)(8) / 6

P(3;2) ≈ 0.180447044