Thread: Uniform random variable question

Suppose that 10^6 people arrive at a service station at times that are independent random variables, each of which is uniformly distributed over (0,10^6). Let N denote the number that arrive in the first hour. Find an approximation for

Hello,

Consider the event : the customer arrives at the first hour, and its complementary : the customer doesn't arrive at the first hour.

Then we have a binomial distribution.
You can approximate it by a Poisson distribution (see here : Binomial distribution - Wikipedia, the free encyclopedia )

I guess I'm just confused by the wording of the question. Is the probability that the customer arrives at the first hour

Originally Posted by Anonymous1

I guess I'm just confused by the wording of the question. Is the probability that the customer arrives at the first hour

Yes (depending on what 10^6 represents...minutes or hours)

And n=10^6

Thanks.

So,



I'm only worried because my answer seems to simple. I don't need to use a summation from 0 to i, do I?

Originally Posted by Anonymous1

Thanks.

So,



I'm only worried because my answer seems to simple. I don't need to use a summation from 0 to i, do I?

No you don't. You're asked the probability for a given i

And it's rather