Square of a standard normal: warmup 1.0 point possible (graded, results hidden) what is the mean and variance of the random variable ? = unanswered unanswered

Step-by-step explanation:

For this case we can use the moment generating function for the normal model given by:

And this function is very useful when the distribution analyzed have exponentials and we can write the generating moment function can be write like this:

And we have that the moment generating function can be write like this:

And we can write this as an infinite series like this:

And since this series converges absolutely for all the possible values of tX as converges the series e^2, we can use this to write this expression:

and we can use the property that the convergent power series can be equal only if they are equal term by term and then we have:

And then we have this:

And then we can find the

And we can find the variance like this :

And first we find:

And then the variance is given by: