1a) Let an experiment consist of rolling three standard 6-sideddice.
i) Compute the expected value of the sum of the rolls.
ii) Compute the variance of the sum of the rolls.
iii) If X represents the maximum value that appears in the tworolls, what is the expected value of X?
1b) Consider an experiment where a fair die is rolled repeatedlyuntil the first time a 3 is observed.
i) What is the sample space for this experiment? What is theprobability that the die turns up a 3 after i rolls?
ii) What is the expected number of times we roll the die?
iii) Let E be the event that the first time a 3 turns up is afteran even number of rolls. What set of outcomes belong to this event?What is the probability that Eoccurs?
