poisson process probability distribution
A shop receives sales according to a Poisson process with rate per minute and suppose each sale, independently of the others, has probability 0.05 of being from a male and probability 0.95 of being from a female.
I'm trying to get the distribution of the number of females sales in the shop in the time interval .
I'm guessing you'd use a Poisson distribution. Someone told me you use an exponential distribution but the exponential is for the times between sales. So I am thinking that the fact that the sales have 0.95 probability of being female affects the rate . So then x the number of female sales in the shop from 0 to t is distributed
Would this be right?