Question

A vendor sells merchandise through Amazon and Ebay. On Ebay she sells an average rate of 2 items per day, while on Amzaon the daily average is 3. Both sales follow a Poisson distribution and are independent of each other. What is the probability that she sells 5 items on a given day?

0.189 is not correct

Answer 1

For X ~ Poi ( ) and Y ~ Poi () ,

X + Y ~ Poi ( + )

So,

For Ebay and Amzaon,

X + Y ~ Poi ( + ) = Poi ( 2 + 3) = Poi ( 5)

P(X) = e^- * ^X / X!

So,

P(X = 5) = e^-5 * 5⁵ / 5!

= 0.1755