A shop opens at 9am and shuts at 5pm. While the shop is open customers arrive as a Poisson process of rate 20 per hour.

a) Calculate the following probabilities:

i) P(no customers enter the shop before 9:03am)

I am confused whether to convert the hours to minutes or not but this is what i have tried.

P(X(1/3)=0)=P(X(1/3)-X(0)=0)=$\displaystyle e^{-1}$

ii) P(exactly 20 customers enter the shop between 2pm and 3pm)

I can work this out if know how to write the above in the form P(X(s+t)=k) etc..

iii) P(exactly 20 customers enter the shop before 11am given that 150 customers

enter during the whole day)

I can work this out if know how to write the above in the form P(X(s+t)=k) etc..

Thanks for any help.