[Queson 2] a) Each the following tables lists certain values of): and their probabilities. Verify whether or not each represents a valid probability distribution. x Pix} 0 0.24 1 0.31 2 0.40 3 0.1!] ii. X P(x) N 0.15 3 0.25 4 0.40 0.20ili. X P(x) C 0.65 0.31 NJ 0.55 3 -0.10iV. X P(x) 2 0.15 3 0.08 4 0.20 0.50b} Two thousand randomly selected adults were asked if they are in favor of or against plagiarism. The following table shows the responses. In Favor Against No Opinion Male 250 600 50 Female 300 700 100 If one person selected at random, nd the probabilitv that this person is i. In favor of plagiarism. ii. Against plagiarism. iii. In favor of plagiarism given that the person is a male. iv. Against plagiarism given that the person is female. v. Female given that the person has no opinion. vi. Has no opinion given that the person is male