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## integration help for expectation of a function of a random variable

hmm...now that I try it fully, that integral doesn't work out. Are you sure you copied down the problem correctly? If yes, then I'm assuming there's a typo because the answer WolframAlpha is giving is:

$$\frac{\pi e^{\frac{1}{2a}} \ \ \ erfc(\frac{1}{\sqrt{2}\sqrt{a}})}{\sqrt{a}}$$, where erfc(z) is the complementary error function. It exists and I've read up on its definition; however, unless your teacher has mentioned it in class yet, I doubt it's the correct answer. Most likely, there's an error the problem you stated.