Thread: standard normal expectations

Calculate , where is the standard normal random variable (with density function ).

So am I to calculate ?

If I'm approaching this correctly, that leaves me with a mess stickier than a barrel of molasses which I don't know how to handle at all. I mean, I know that the integral of f(x) is F(x) where F(x) is the cumulative distribution function for the standard normal distribution, but I don't know what that is explicitly nor how to calculate it, let alone what is being asked here. In lecture, we have used tables of values for , where (I assume) is this F(x), to approximate definite integrals of f(x) but I do not see how that might help here...so lost.

Suggestions, please?

Your problem might be asking you to evaluate:

Originally Posted by qmech

Your problem might be asking you to evaluate:

and instead of completing the square, blah blah, to make this a valid density

NOTE that this is just the MGF evaluated at t=1.

Originally Posted by matheagle

and instead of completing the square, blah blah, to make this a valid density

NOTE that this is just the MGF evaluated at t=1.

Thanks for your replies.

I assure you both, however, that I am stating the problem correctly. In fact, there is another problem I have that requires computing a similar integral (which I can only take as evidence that is not a typo). To further complicate things, MGFs have not been an addressed topic so I must further assume that a solution is intended to be MGF-free.

I really do appreciate your replies, and if you have any further advice would love to hear it.