00:01
So the gamma distribution equation itself is pretty complicated.
00:04
So what i'll be doing is using this online calculator here.
00:08
We can see that we have the shape parameter and scale parameter that we need to input.
00:13
But we're told the mean value and the variance instead.
00:17
So we have that for a gamma distribution.
00:21
The mean is going to be k times theta, or in terms of the notation on that calculation.
00:31
It's a times b the shape times the scale and the variance is going to be a times b squared so we know that for our situation given we have that the mean is nine seconds the variance is 27 seconds so if we did for example a times b squared divided by a times b we can see that that would just give us b and so that would be our variance divided by our mean, so that would be 27 over 9, which gives us that our b value is going to be 3, i believe.
01:10
Yep.
01:11
So our b value is equal to 3.
01:13
Then having that, you can see that, well, a times b needs to be equal to 9, so we can conclude that in addition, our scale parameter must be 3 as well.
01:25
Now, going back to our gamma distribution calculator, we put in shape parameter 3, scale parameter 3, the initial percentile that we're looking for...