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A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let L be the number of tosses to get this first ‘Head’. The entropy H(L) in bits is _________

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In this problem random variable is L

L can be 1,2,..............

P{L = 1} = 1/2

P{L = 2} = 1/4

P{L = 3} = 18

H{L} = 1/2log21/(1/2) + 1/4log21/(1/8) + ..... = 0 + 1 x 1/2 + 2 x 1/4 + 3 x 1/8 + ...

[Arithmatic gemometric series summation]

= 2/(1 - 1/2) + (1/2 x 1)/(1 - 1/2)2 = 2

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