# moment generating functions by integration

Let X~N(0,1)m find the moment generating function of $X^2$ using integration techniques.

I'm not sure exactly what this is asking me to do. Is $X^2$ just the pdf for the standard normal function squared? Any pointers appreciated!

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Is $X^2$ just the pdf for the standard normal function squared?
If you mean the pdf of $X^2$, then no. $X^2$ will follow a $\chi^2$ distribution with one degree of freedom. You can't find pdfs of transformed variables simply by applying the transformation to the pdf of the original variable.
$$\mathbb E[e^{tX^2}].$$ You can find this by integration just like you would any other expectation of a function of $X$:
$$\mathbb E[e^{tX^2}] = \int e^{tx^2} f_X(x)\, dx,$$ where $f_X(x)$ is the standard normal pdf.