# Thread: problem on gamma distribution

1. ## problem on gamma distribution

let be 'n' i.i.d random variables, each following gamma (1,3) distribution.
show that

2. ## Re: problem on gamma distribution

Just a quick question. The gamma gets parameterized in different ways. Which way are you using? Is the expected value of your gamma 3 or is it 1/3?

3. ## Re: problem on gamma distribution

i mean the distribution is:-

i mean the expected value is 1/3

4. ## Re: problem on gamma distribution

Ah. Then yes you should really tell us that info because apparently your parameterization is different than the two I was thinking of. To me you have alpha and beta mixed up using the first parameterization I was thinking of. But that doesn't matter too much.

The next step is realizing that since these are independent and share the same parameters you can figure out the distribution of the sum.

5. ## Re: problem on gamma distribution

yes the sum follows a gamma (1,3n) in my notation (that is, expectation is 1/3n). right?

6. ## Re: problem on gamma distribution

Originally Posted by Sambit
yes the sum follows a gamma (1,3n) in my notation (that is, expectation is 1/3n). right?
Well you got the sum right but your expectation doesn't look right to me. I would think the expectation is 3n.

7. ## Re: problem on gamma distribution

i think the two of us are using different notations. i mean the sum has the distribution

now is that what you got?

8. ## Re: problem on gamma distribution

Expectation is still 3n. http://en.wikipedia.org/wiki/Gamma_distribution. Once I saw the way you parameterize it and how the distribution looks I understand what's going on. All that's happening is you're putting what I call alpha in the second parameter spot, which is where I would put what I call beta. Wikipedia uses different parameter names but it agrees with me. The expectation is the product of the parameters in both our cases. 1*(3n) = (3n)*1 = 3n.

9. ## Re: problem on gamma distribution

yes. sorry i was wrong. it was a mistake...
what now?

i am writing gamma(alpha, p). i mistakenly wrote the expectation as alpha/p,, which is actually p/alpha. clear?
sorry for the confusion

10. ## Re: problem on gamma distribution

No need to worry. From there I'm not exactly sure where it should go but it does simplify the problem I believe. It looks like Chebyshev's inequality might help but I can't guarantee that that'll work perfectly for you. I'd have to get out some paper and try things out myself. Have you learned chebyshev's inequality?

yes i have.

12. ## Re: problem on gamma distribution

See if you can massage it into the framework to apply chebyshev. Note that the standard deviation of the distribution is

13. ## Re: problem on gamma distribution

not getting.

here so we have
i don't think it helps...

14. ## Re: problem on gamma distribution

i have done it in a separate way:-

>1/2
this can be done, isn't it?

15. ## Re: problem on gamma distribution

http://en.wikipedia.org/wiki/An_ineq...and_the_median

Let be the median of
Here using the Chebyshev's/Jensen's Inequality, we get

Then,