# Thread: Gamma random variable problem

1. ## Gamma random variable problem

Question: Let X be a gamma random variable with $\displaystyle \mu$ = 21 and $\displaystyle \sigma^2$ = 63. Find P(18$\displaystyle \leq$X$\displaystyle \leq$30).

I have calculated that $\displaystyle \beta$=3 and $\displaystyle \alpha$=7

but I'm not sure how to turn the interval 18 to 30 into some interval I can find in the tables.

Can you help?

2. ## Re: Gamma random variable problem

You say "the tables" as if we are looking at them too, or all tables have the same contents.

if i was using my tables (Tables and formulae for UK actuarial exams) i would use the following relationship:

$\displaystyle \text{if } X \sim \chi ^2 (v) \text{ then } cX \sim \Gamma(0.5v,2c)$

This can be used to re-express your gamma probability as a chi-square probability. Chi-square distributions are tabulated.

If this isn't familiar, I assume your professor showed you one before giving you the question? how did he do it?

3. ## Re: Gamma random variable problem

Sorry. All I have been given is an Incomplete Gamma Function Table where 1<=y<=15 and 1<=alpha<=10. Can I subtract 30-18 and use the value of 12 on this table? or am I way off.