Exercise 17 (#1.46). Let X, and X2 be independent random variables having the standard normal distribution. Obtain the joint Lebesgue density of (Y1, Y2), where Yi = VX7 + X? and Y2 = X1/X2. Are Y, and Yz independent? Note. For this type of problem, we may apply the following result. Let X be a random k-vector with a Lebesgue density fx and let Y = g(X), where g is a Borel function from (R*, B*) to (R*, B* ). Let A1, ...; Am be disjoint sets in B' such that RK - (A] U . . . U Am) has Lebesgue measure 0 and g on A; is one-to-one with a nonvanishing Jacobian, i.e., the determinant Det(Og(x)/0x) # 0 on Aj j =1. .... m. Then Y has the following Lebesgue density: fv(x) = ) Det (Oh; (x)/0r) fx (h;(x)), j=1 where h; is the inverse function of g on Aj, j = 1, .... m.20WI Assignments 3.3.1 Counting principles 3.3.1 Counting principles Counting with permutations Question There are 9 players on a youth baseball team. To create the lineup, the coach chooses three players to play pitcher, catcher, and first base. How many ways can the coach choose these three positions? Provide your answer below