GATE 2015 SET-2 Q 29

Question

Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.

Comments

https://gateoverflow.in/20011/tifr2011-a-6

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For more such problems: https://www.codechef.com/wiki/tutorial-expectation

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I think here the random variable concept is there. So I have provided my answer. Please correct me if I am wrong.

Answer 1

X= No of times coin is tossed.

X=2,3,4..

    X          2              3               4                   5          .........

P[X=x]    (1/2)^2    (1/2)^3   (1/2)^4       (1/2)^5    .........

E[x] = 2*(1/2)^2 + 3*(1/2)^3  + 4*(1/2)^4 + 5*(1/2)^5 + .....

This is an AGP. On solving this gives

E[x] = 1.5

Comments

where to learn the AP AND GP topic

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It should be 6.

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2(2^2-1)