1. ## Probability in geometric

Hello,

In the family with geometric distribution population average is 3 .
The probability what percentage families exactly has 3 population?

(Average in geometric distribution is 1/p , now we have 1/p = 3 , true? now how can calculate p ?)

Thanks

2. ## Re: Probability in geometric

since no families have 0 members the support for this distribution will be the positive integers

thus the mean is given by

$E[N] = 3=\dfrac 1 p$

where $p$ is the distribution parameter.

so $p=\dfrac 1 3$

$f_N(n) = (1-p)^{n-1}p$

so

$f_N(3) = \left(\dfrac 2 3\right)^{2}\left(\dfrac 1 3\right) = \dfrac{4}{27}$

3. ## Re: Probability in geometric

Thank but if we want "The probability what percentage families smaller than has 3 population?"

4. ## Re: Probability in geometric

Then calculate P(0), P(1), and P(2) and add!

5. ## Re: Probability in geometric

Thanks you and it's OK, but suppose we have
"The probability what percentage families smaller than has 10 population?"

Now it's hard , calculate 10 independent probability .

6. ## Re: Probability in geometric

Originally Posted by life24
Thanks you and it's OK, but suppose we have
"The probability what percentage families smaller than has 10 population?"

Now it's hard , calculate 10 independent probability .
Hello,

7. ## Re: Probability in geometric

Why is it hard? It's just adding a few terms. Even more simple, it's adding a few terms of a geometric series.

8. ## Re: Probability in geometric

Originally Posted by Archie
Why is it hard? It's just adding a few terms. Even more simple, it's adding a few terms of a geometric series.
Perhaps we want smaller than has 100 population. So we should calculate 100 expression independent and then added together?>

9. ## Re: Probability in geometric

Has addition become difficult? Or are you just lazy?

If you really want to be lazy, you have to be awake enough to remember how to sum the terms of a geometric progression.

10. ## Re: Probability in geometric

Originally Posted by HallsofIvy
Then calculate P(0), P(1), and P(2) and add!
If we want calculate ' Maximum population is 3' is the same with 'Smaller than 3 population' ?
Thanks

11. ## Re: Probability in geometric

Originally Posted by life24
If we want calculate ' Maximum population is 3' is the same with 'Smaller than 3 population' ?
Thanks
No, "maximum population is 3' would be P(0)+ P(1)+ P(2)+ P(3). "Maximum population is 3" means "smaller than or equal to 3.