You are a contestant on a TV game show, there are four identical-looking suitcases containing $200, $400, $800, and $1,600. You start the game by randomly choosing a suitcase. Among the three unchosen suitcases, the game show host opens the suitcase that holds the least money. The host then asks you if you want to keep your suitcase or switch one of the other remaining suitcases. For the following analysis, use the following notation for events: A) C is the even that you choose a suitcase with i dollars.
B) O; denotes the event that the host opens a suitcase with i dollars.
C) R is the reward in dollars that you keep.
1) You refuse the host's offer and open the suitcase you first chose. Find the Probability Mass Function (PMF) of R and the expected value E[R].
2) You switch and randomly choose one of the two remaining suitcases. You receive the R dollars in this chosen suitcase. Find the Probability Mass Function (PMF) and expected value of R.