Assignment #1      In each of the following problems find the answer in two ways.         a) Think and use the sum principle E(X + Y) = E(X) + E(Y)         b) Write ISETL code to simulate the experiment and the random            variable. You should !include some files such as cards.utl1. A forgetful waiter gives 4 orders, at random, to 4 people at a table.   Assume that all the orders are different. You will get $1 for each   order that is given to the correct person. What is the fair price to   pay to play this game?2. When a red die comes up with an odd number you get $1; when a small   die comes up with a even number you get that number of dollars.   What is the fair price when a large red die a small white one are   rolled together?   What is the fair price if one small red die is rolled?3. A die is rolled and you collect $1 if a six comes up and $0 if anything   else comes up. What is the fair price for this game?4. A die is rolled. If it comes up six then six coins are tossed; if no   six comes up then one coin is tossed. You will get a dollar for each   head that appears on the coins. What is the fair price to pay to play   this game?5. Cards are removed from a standard deck until an ace is removed; you   collect $1 for every non-ace that was removed. What is the fair price   for this game?