# Graph of pdf and calculate moments

http://www.dumpt.com/img/viewer.php?file=0pt0l719ug05g1r09sly.jpg

The diagram in the link shows the graph of a probability density function. Given that the mean is zero, express $b$ in terms of $a$. Calculate the second and third moments in terms $a$.

I have found that $b=2a$. I am not sure how to find moments from a pdf graph.

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Please make your question self-contained. – Did Feb 14 '13 at 15:49

I am pretty sure your value for $b$ is wrong. How did you get it?
I used $-ac+(1/2)bc=0$ because the mean is zero. – bbr4in Feb 4 '13 at 8:46
The problem is (as I assume you mean by 'that's wrong') that $ac+(1/2)bc=0$ doesn't make the mean zero. Note that you need to make the area 1 and the mean 0, which lets you get both $b$ and $c$ in terms of $a$. Once you have $b$ and $c$ you can find the pdf (which is still depends on $a$) quite easily. There, $a$ takes the role of a parameter. Imagine that given $b$, and $c$ and some particular value for $a$, the density is $f(x)$. How would you work out the mean if you knew what $f$ was? – Glen_b Feb 4 '13 at 21:42