4. If you study heat conduction in physics, you are likely to encounter the CRV Y with pdf f (y) = 2-32 /2, y > 0 TT else a. Find E(Y) by evaluating an integral by hand. (As always, use beautiful notation to deal with the improperness of the integral. It's time to get serious about presenting your work.) b. Suppose your friend wasn't able to do part a and suggested, instead, to use a single value, Y1, from the distribution to build a confidence interval [Y1, 2 . Yi] that would hopefully contain the answer from part a. What is the confidence level of this confidence procedure? (You will need to use your answer from part a.) Hint: About halfway through the problem, you will be faced with a difficult integral. If you write down the pdf of Z ~ N(0, 1), you'll notice your integral is very similar to the pdf of Z, and this observation offers a way forward. [Tables not tech]