Consider a 6-face die {1,2,3,4,5,6} is constructed so that the odd numbers are twice as likely to occur as the even numbers. Define X as the number turning up in a toss. 1. Find the probability distribution function of X. 2. Define the event A is the toss of the die results in a number greater than 3 . Define the event B is getting a perfeet square when a die is tossed. Find the conditional probability P(B∣A). 3. Are events A and B independent? Show the proof.