please i need help with these questions 1,2,3

1. A die is rolled and, independently, a coin is tossed. Let X be the value of the die if the coin is H and minus the value of the die if the coin is T. (a) Calculate and plot the PM of X. (b) Calculate E [X] and var (X) (c) Calculate and plot the PMF of X2 2X. 2. A drunk walks down a street. Assume he starts at block 0. Every 10 minutes, he moves north a block (+1) with probability p or south a block (-1) with probability 1 p, independently of any movement outside of those 10 minutes. (a) What' 5 the PMF of his position after 1011 minutes? (b) Where would you expect him to be in an hour? 3. Legend has it, a Jinn was fond of probability. Those unfortunate enough to encounter it in the desert, were given an intriguing offer: In this desert old, Without rain, as told, Rains one, is arid ten, I will take one of ten, Give me all your gold, And 1when rain, behold, And I will make one ten! What is left is therein. Distrustful of poetic spirits, travelers were quick to turn down this offer and to con- tinue their journey, amusing the Jinn to no end. You've taken ECE 341 and are not so dismissive. You interpret the fact that \"for every 1 day that it rains 10 do not\" by the appropriate probability p of rain happening independently every day. You know that if you give x amount of gold to the Jinn, you'll end up with 10x gold at the beginning. But every day that it doesn't rain, you will lose 10% of what remains. Until it rains, at which point you get to keep whatever remains. Assume gold can be divided arbitrarily. Starting with x gold, calculate the expected amount of gold left at the end. Do you give your gold to the Jinn