Question

The table below shows the probability distribution of a random variable X. XP(X) – 120.42 – 110.08 – 100.5 What is the expected value of X? Write your answer as a decimal.

Answer 1

Answer:

The expected value of X = 109.2

Step-by-step explanation:

We can find the expected value of X by using this formula:

$\boxed{\mu=\Sigma x_i\cdot p_i}$

where:

• $\mu$ = expected value
• $x_i$ = value of an outcome
• $p_i$ = probability of an outcome

Given:

$\begin{array}{c|c|c|c} X & 120 & 110 & 100\\\cline{1-4} P(X) & 0.42 & 0.08 & 0.5\\\end{array}$

• $x_1=120$
• $p_1=0.42$
• $x_2=110$
• $p_2=0.08$
• $x_3=100$
• $p_3=0.5$

Hence:

$\mu=\Sigma x_i\cdot p_i$

  $=x_1\cdot p_1+x_2\cdot p_2+x_3\cdot p_3$

  $=120(0.42)+110(0.08)+100(0.5)$

  $=\bf 109.2$