M= 2 Question 1: (40 Points, 5 points each part) -2.8 In a basket there are 15 identical balls, 5 red balls, 5 black balls and 5 white balls. The balls of each color are numbered from 1 to 5. You randomly select two balls with replacement. Let random variable X denote the number on the first selected ball, and random variable Y denote the number on the second selected ball. a) Draw the tree diagram of this experiment, and identify all probabilities. b) What is the probability mass and cumulative table (function) of X? text c) What is the probability that the second selected ball is red and less than A (A is the mean of your ID numbers)? d) Given that the first ball was 4, what is the probability that the second ball is more than A/2? e) Given that the first ball was 3, what is the probability that the second ball is not 3? f) Find the expected value of Y. g) Find the variance of Y. h) Are X and Y independent? Show your work