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1. Suppose we toss a coin 100 times. Let X = the number of heads in the 100 tosses.
a. What is the PMF of X?
b. find the probability if X = 50.
c. find the probability if X ≤ 50.
2. A box contains five keys, two of which will open a lock. The keys are randomly selected and tried one at a time until the lock is opened. Keys that do not open the lock are discarded. Let X = the number of the trial on which the lock is opened. Find the expected number of trials until the lock is opened, E[X]. You will need to find the PMF PMF ????(???? = ????) in order to do so.
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