Let Y = a + bZ + cZ2 where Z (0,1) is a standard normal random variable.(adsbygoogle = window.adsbygoogle || []).push({});

(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 part of the question involving E[Z^3] and E[Z^4]. Clearly E[Z]=0 and E[Z^2]=1 but I do not no where to proceed when computing higher powers of Z. Any help would be greatly appreciated.

Thanks

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# Homework Help: Expectation of Normal Distribution

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