Question

No. of birthday parties observed in a class is a poisson random variable with an average of 6/month. what is the probability that there will be 3 parties in a day?

Answer 1

Average amount of parties in a day $\lambda=6/30=0.2$

According to Poisson's distribution:

$P(3)=\lambda^3e^{-\lambda}/3!=0.2^3e^{-0.2}/6\approx\\ \approx0.001091641\approx0.11\%$