Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. Is the number of fish caught during a fishing tournament a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable C. It is not a random variable b. Is the number of textbook authors now sitting at a computer a discrete random variable, a continuous random variable, or not a random variable? O A. It is a continuous random variable. O B. It is a discrete random variable O C. It is not a random variable c. Is the ~NR 2 a discrete random variable, a continuous random variable, or not a random variable? O A. It is a continuous random variable, O B. It is a discrete random variable O C. It is not a random variableExercise 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