please answer all the questions, especially the first one.

10. In this question we take a closer look at prediction intervals. Let 0 = Bo + BIX, and let 0 = Bo + 31Xx. Thus, Y. = 0 while Yx = 0 + E. Now, 0 ~ N(0, se2) where se? = V(0) = V(Bo + BIZ*). Note that V(0) is the same as V(Y,). Now, 042\\V(0) is an approximate 95 percent confidence interval for 0 = Bo + 31, using the usual argument for a confidence interval. But, as you shall now show, it is not a valid confidence interval for Y*. (a) Let s = VV(Y*). Show that P ( Y x - 25