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\fa. Solve for the value of k for the probability mass function to be legitimate. b. Construct its probability distribution (table) c. Construct its probability histogram. d. Solve for the expected value and variance of the random variable X. 2. Given the probability distribution: X 0 1 2 3 4 f(x) 2 5 N 15b 18 ga 18 Hint: the value of b is twice the value of a a. Solve for the value of a and b for the discrete probability distribution to be legitimate, b. Solve the expected value, variance and standard deviation of the random variable X. 3. The officers of the Mathematics Club are planning to sell 280 tickets to be raffled during the school's foundation day. One ticket will win P5,000, two tickets will win P3,000, three tickets will win P2,000 and the other tickets will win nothing. If you will buy one ticket, what will be your expected value and variance of his gain? 4. You play a game with two six-sided dice. If you roll a sum of 5 or 7, you win P400. If you roll a sum of 6 or 8, you win P300. If you roll a sum of 11 or 12, you win P200. However, you lose P250 for anything else. If you continue to play the game, how much do you expect to win or lose in the game? Will you encourage your friend to play that kind of game? Why or why not