Question

A fair 4-sided die is tossed. If X denotes the random variable giving the number on the bottom face of the die, find E(X). E(X)

Answer 1

Answer:

$E(x) = \frac{5}{2}$

Step-by-step explanation:

Given

$Die = 4\ sided$

$Side = \{1,2,3,4\}$

Required

Determine E(x)

E(x) is calculated as thus:

$E(x) = \sum x.f(x)$

Since the die is fair.

$f(x) = \frac{1}{4}$ for all sides of the die

So, we have:

$E(x) = \sum x.f(x)$

$E(x) = 1 * \frac{1}{4} + 2 * \frac{1}{4} + 3 * \frac{1}{4} + 4 * \frac{1}{4}$

$E(x) = \frac{1}{4} + \frac{2}{4} + \frac{3}{4} + \frac{4}{4}$

$E(x) = \frac{1+2 +3+4}{4}$

$E(x) = \frac{10}{4}$

$E(x) = \frac{5}{2}$