retagged by
648 views
1 votes
1 votes

I always do expected value questions wrong. Please suggest a detailed way to solve these questions.

Suppose a coin is tossed 9 times, with the result

$HHHT T T T HT$

The first set of three heads is called a run.There are three more runs in this sequence, namely the next four tails, the next head, and the next tail. We do not consider the first two tosses to constitute a run, since the third toss has the same value as the first two.

Now suppose an experiment consists of tossing a fair coin three times. Find the expected number of runs

retagged by

1 Answer

1 votes
1 votes

It is an example of discrete probability as no of runs will be an integral value ranging from 1 to 3..

So P(1 run)   =  P(TTT) + P(HHH)

                    = 1 / 4

    P(2 runs)   = P(HHT) + P(THH) + P(TTH) + P(HTT)

                    =  2 / 4

    P(3 runs)   =  P(HTH)  + P(THT)

                    =  1 / 4

Therefore expected number of runs , meaning

 E(run)          = Σ (no of runs) * P(no of runs)

                    = (1 * P(no of runs = 1)) + (2 * P(no of runs = 2)) + (3 * P(no of runs = 3))

                    =  (1 * 1 / 4)  +  (2 * 2 / 4) + (3 * 1 / 4)

                    =  (1 / 4) + (4 / 4) + (3 / 4)

                    =  8 / 4

                    =  2

                    

Hence , expected no of runs  =  2

           

Related questions

0 votes
0 votes
1 answer
1
dd asked Sep 27, 2016
950 views
If n balls are randomly selected from an urn containing N balls of which m are white,find the expected number of white balls selected.