Stats help required

Question

Stats help required

hba · Answer

attachment

anonymous · Answer

does this have to do with moment generating functions.

hba · Answer

Moments,Yes.

anonymous · Answer

hmm, our class is just covering transformations of random variables and distribution method.

kirbykirby · Answer

What's a moment ratio?

anonymous · Answer

look it up on google.

hba · Answer

Um,I don't know.

kirbykirby · Answer

Is it the same as an L-moment ratio, which keeps popping up on google

anonymous · Answer

appears so.

anonymous · Answer

take the first and second moments!

anonymous · Answer

keep it simple.

hba · Answer

@electrokid How?

kirbykirby · Answer

Well the first moment would be your mean, which should be $2r^2$, but I don' know how you can determine the second moment without knowing the pdf or cdf (or anything else) about he distribution o_O

anonymous · Answer

hold on,
about the notation,
$\mu_k$ is also used to represent the k^th moment!

kirbykirby · Answer

oh they're using that notation.

anonymous · Answer

otherwise, use the regular formula
$$
{\rm moment}=\int_{-\infty}^\infty(x-\mu)^k(2x^2)dx
$$

anonymous · Answer

this will give you the k^th moment.

anonymous · Answer

variance is your second moment, k = 2

hba · Answer

@electrokid 

I ain't getting anything.

anonymous · Answer

k=3 -> skewness
kurtosis and so on

hba · Answer

Can we get to the ques?

anonymous · Answer

tell me, what does $\mu_r$ represent?

hba · Answer

r'th moment.

anonymous · Answer

aha. then no need for the integration

1st moment = mean -> plug in r = 1
2nd moment = variance -> plug in r=2
3rd moment = skewness -> plug in r = 3

hba · Answer

Okay so i got 1st moment as 2,Second moment as 8 and third moment as 18.

hba · Answer

Now what?

hba · Answer

@electrokid