D Question 1 1 pts Probability Density Function (PDF): Given a random variable X with the PDF defined as f (x) = ( 1+2) compute the probability P(-2 for x 2 0 and F(x) = 0 for x 1) for 1 = 2. Oel Oe-2 O1-e-1 O1-e-2D Question 3 1 pts Bayes' Rule: Suppose two events A and B in a probability space, where P(A) = 0.3, P(B) = 0.4, and P(An B) = 0.15. What is P( A B) ? O 0.45 O 0.5 O 0.55 O 0.375 D Question 4 1 pts Rank and Singular Value Decomposition (SVD): Let A be a 3 x 3 matrix with eigenvalues X1 = 1, 12 = 2, and 13 = 0. What is the rank of A? 0 3 OO 02 O 1\f