I have the following question; Assuming there are a stream of people entering a shop at a Poisson process of rate 5 per second. The arrival requests are in 3 categories:
Girls with probability 0.5
Ladies with probability 0.3
Women with probability 0.2
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In order to know the probability that any given request will be
followed by another one within half a second will be ?So here what i think the result will be is : T~Exponential(5) so P(T<0.5"half a second")
= 0.5 -exp^-5 => 0.4932. -
But how can i know, the mean arrival time between two successful
women arrivals ? - And also how can i know the probability that there are 6 ladies
arriving in a 10 second period ?
Best Answer
You can answer these with rates:
Overall $5$ females per second, so $2.5$ per half-second, and the probability of no females in a half-second is $\exp(-2.5)$
Women arrive at a rate of $0.2 \times 5=1$ per second, so the expected time between women is $\frac11=1$ second
Ladies arrive at a rate of $0.3 \times 5=1.5$ per second, so $15$ per ten seconds, the the probability of $6$ per ten seconds is, from the Poisson distribution, $\exp(-15)\frac{15^6}{6!}$