# poisson process probability distribution

• Apr 20th 2006, 09:02 PM
emterics90
poisson process probability distribution
A shop receives sales according to a Poisson process $\displaystyle \{N_t : t \ge 0\}$ with rate $\displaystyle \lambda=1$ 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 $\displaystyle [0,t]$.

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 $\displaystyle \lambda$. So then x the number of female sales in the shop from 0 to t is distributed

$\displaystyle f(x)=\frac{e^{-0.95 \lambda t}(0.95 \lambda t)^x}{x!}$

Would this be right?
• Apr 21st 2006, 04:13 AM
CaptainBlack
Quote:

Originally Posted by emterics90
A shop receives sales according to a Poisson process $\displaystyle \{N_t : t \ge 0\}$ with rate $\displaystyle \lambda=1$ 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 $\displaystyle [0,t]$.

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 $\displaystyle \lambda$. So then x the number of female sales in the shop from 0 to t is distributed

$\displaystyle f(x)=\frac{e^{-0.95 \lambda t}(0.95 \lambda t)^x}{x!}$

Would this be right?

Looks OK to me.

RonL