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Mathematical Statistics question.

24/09/2020 Client: murali Deadline: 3 days

  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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