Question

If a die is thrown at random, then the expectation of the number on it is ______.

Options

• 2.4

• 3.3

• 2.1

• 3.5

Answer 1

If a die is thrown at random, then the expectation of the number on it is 3.5.

Explanation:

A die is thrown

Random variable X = 1, 2, 3, 4, 5, 6

X	1	2	3	4	5	6
P(X)	${\displaystyle \frac{1}{6}}$	${\displaystyle \frac{1}{6}}$	${\displaystyle \frac{1}{6}}$	${\displaystyle \frac{1}{6}}$	${\displaystyle \frac{1}{6}}$	${\displaystyle \frac{1}{6}}$

E(X) = ∑ P(X) (X)

${\displaystyle =1\times \frac{1}{6}+2\times \frac{1}{6}+3\times \frac{1}{6}+4\times \frac{1}{6}+5\times \frac{1}{6}+6\times \frac{1}{6}}$

${\displaystyle =\frac{1}{6}(1+2+3+4+5+6)}$

${\displaystyle =\frac{1}{6}\times 21=\frac{7}{2}=3.5}$