Question

$2$ dice are thrown. Suppose a random variable $X$ is assigned a value $2k$ , if the sum on the dice is equal to $k$ , then the expected value of $X$ is

• A. $10$
• B. $12$
• C. $14$
• D. $\frac{50}{9}$

Answer 1

Answer: (C)

$k$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$P\left(k\right)$	$\frac{1}{36}$	$\frac{2}{36}$	$\frac{3}{36}$	$\frac{4}{36}$	$\frac{5}{36}$	$\frac{6}{36}$	$\frac{5}{36}$	$\frac{4}{36}$	$\frac{3}{36}$	$\frac{2}{36}$	$\frac{1}{36}$

$k=$ sum on dice
Expected value $=\frac{1}{36}\times 4+\frac{2}{36}\times 6+\frac{3}{36}\times 8+\frac{4}{36}\times 10$
$+\frac{5}{36}\times 12+\frac{6}{36}\times 14+\frac{5}{36}\times 16+\frac{4}{36}\times 18$
$+\frac{3}{36}\times 20+\frac{2}{36}\times 22+\frac{1}{36}\times 24$
$=\frac{504}{36}=14$