Question

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 :

• A. $\frac{1}{8}$
• B. $\frac{3}{16}$
• C. $-\frac{1}{8}$
• D. $-\frac{3}{16}$

Answer 1

Answer: (A)

$\frac{1}{8}$

Answer 2

Expected value $= \sum \,XP\left(k\right)$
$-\frac{1}{32}-\frac{12}{32}-\frac{11}{32}+\frac{15}{32}+\frac{8}{32}+\frac{5}{32}$
$= \frac{28-24}{32} = \frac{4}{32} = \frac{1}{8}$