Recent content by MattFox

Or more accurately, what form the solution will take i.e an integer, function of Z...

F(z) is the cdf of the normal distribution. So E(Z^3) = Z^3 * F(Z) - INT 3Z^2 * F(Z). Do i then need to apply integration by parts again? I'm sorry if I'm asking too many questions I just really don't understand what I'm trying to achieve as a solution.

Ok so, INT u dv = uv - INT v du Then i let u = Z^3 and dv = the pdf of the normal dist. Im lost when it comes to integrating the pdf and I'm not sure how it will condense down to a manageable solution. Sorry about the lack of symbols, I'm not sure how to properly upload images yet.

I'm not really getting anywhere with the integration by parts. Is there any hint you could offer or show me a step I could be missing out?

So am I right in thinking I let g(z) = z^3 and f(z)= 1/(sigma * sqrt2pi) ... and then use integration by parts?

Let Y = a + bZ + cZ2 where Z (0,1) is a standard normal random variable. (i) Compute E[Y], E[Z], E[YZ], E[Y^2] and E[Z^2]. HINT: You will need to determine E[Z^r], r = 1, 2, 3, 4. When r = 1, 2 you should use known results. Integration by parts will help when r = 3, 4. I am struggling with the...