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An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k=3,4,5, otherwise X takes the value-1. Then the expected value of X is

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$\frac{1}{8}$

$\frac{3}{16}$

$- \frac{1}{8}$

$- \frac{3}{16}$

answer is A.

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Detailed Solution

k	0	1	2	3	4	5
P(k)	$\frac{1}{32}$	$\frac{12}{32}$	$\frac{11}{32}$	$\frac{5}{32}$	$\frac{2}{32}$	$\frac{1}{32}$

Expected value $= \sum X P (k)$

$= (- 1) \times \frac{1}{32} + (- 1) \times \frac{12}{32} + (- 1) \times \frac{11}{32} + (3) \times \frac{5}{32} + (4) \times \frac{2}{32} + (5) \times \frac{1}{32} = \frac{1}{8}$

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