Problem 2 (10 pts) Variance 02 = E[[X [if] {where p. = EX) tells you how far the distribution is spread out of from its mean. Similarly, E[[X arts] which it taste stress, tells you how heavy the tail of your distribution is. We say a distribution has a heavy tail if its density is relatively large on the points that is far away from the mean. For example, kurtosis of eiqjonential random variable and normal random variable are 6 and 3, respectively. In fact, exponential distribution has heavier tail than normal random variables as you can see in the following gure. IBM DIM ll'll \"III \"I? EM am In this question, you will show that kurtosis of normal random variables is 3, using some facts you learned in this class. You may nd page 358 ass of the textbook helpful. Suppose X, v E Nut, 91}. You may use the result from previous parts even if you oouldn't solved them. a] lpt What is the (lensit of R = 2 + Y_'-\" 2 and What is the name of this distri y 0' ' bution? Proof is not required. (all) {lpt} What is the density of 5' = R2 ? Provide the name and the parameter of this distribution. Proof is not required. (b) (4pts) Show that as? = s