Consider the following joint pdf of Gender (X = 1 if female, X = 0 if male) and GPA (Y, with possible values 1,2,3,4). The joint pdf f(x, y) is given: Y (GPA) 1 2 3 4 f(x) X = 1 (female) 0.025 0.075 0.25 0.15 X (sex) X = 0 (male) 0.05 0.1 0.225 0.125 f(y) Find the marginal pdf f(X = 1), that is, find the probability that a randomly drawn student from this population is female. Select one or more: a. f(X = 1) = 0.4 b. f(X = 1) = 0.6 c. f(X = 1) = 0.275 d. f(X = 1) = 0.5Let X, Y be two random variables, with joint pdf f(@, y), and marginal pdfs f(x), f(y). We say that X and Y are statistically independent if Select one or more: a. f(x y) = f(x) b. f(x, y) = f(x) c. f(xly) = f(y) d. f(x, y) = f(x) . f(y)Consider the following joint pdfs of Gender (X = 1 if female, X = 0 if male) and GPA (Y, with possible values 1,2,3,4). Which of the following joint pdfs describe X and Y that are independent? Select one or more: a. Y (GPA) 1 2 3 4 f(x) X = 1 (female) 0.02 X (sex) 0.06 0.2 0.12 X = 0 (male) 0.06 0.12 0.27 0.15 f(y) b. Y (GPA) 1 2 3 4 f( x) 0.025 0.075 0.25 0.15 X (sex) X = 1 (female) X = 0 (male) 0.05 0.1 0.225 0.125 fly) C. Y (GPA) 1 2 3 4 f(x) X = 1 (female) 0.02 0.06 X (sex) 0.2 0.12 X = 0 (male) 0.03 0.09 0.3 0.18 f(y) d. Y (GPA) 1 2 3 4 f(x) X =1 (female) 0.04 0.08 0.18 0.1 X (sex) X = 0 (male) 0.06 0.12 0.27 0.15 fly)Consider the following joint pdf of Gender (X = 1 if female, X = 0 if male) and GPA (Y, with possible values 1,2,3,4). The joint pdf f(x, y) is given: Y (GPA) 1 2 3 4 f(x) X =1 (female) 0.025 0.075 0.25 0.15 X (sex) X =0 (male) 0.05 0.1 0.225 0.125 F(y) Find the marginal pdf f(Y = 4), that is, find the probability that a randomly drawn student from this population has GPA of 4. Select one or more: a. f(Y = 4) = 0.5 b. f(Y = 4) = 0.6 C. f(Y = 4) = 0.275 d. f(Y = 4) = 0.4Consider the following joint pdf of Gender (X = 1 if female, X = 0 if male) and GPA (Y , with possible values 1,2,3,4). The joint pdf f(x, y) is given: Y (GPA) 1 2 3 4 f(x) X (sex) X = 1 (female) 0.025 0.075 0.25 0.15 X = 0 (male) 0.05 0.1 0.225 0.125 f(y) Which of the following tables depict the conditional distribution of GPA given gender, f(ylx) ? Select one or more: a Y (GPA) 1 2 3 4 fly | X=1) 0.05 0.15 X (sex) 0.5 0.3 fly | X=0) 0.1 0.2 0.45 0.25 b Y (GPA) 1 2 3 4 0.2 X (sex) f(y | X=1) 0.1 0.45 0.25 f(y | X=0) 0.05 0.15 0.5 0.3 C. Y (GPA) 1 2 3 4 X (sex) fly | X=1) 0.05 0.15 0.5 0.25 fly | X=0) 0.1 0.2 0.45 0.3 d. Y (GPA) 1 2 3 4 f(y | X=1) 0.05 0.15 0.5 0.3 X (sex) fly | X=0) 0.05 0.2 0.45 0.25