Question

select the correct answer
what is the expected value of an original investment of $3,000 that has a 10% chance of ending up with a value of $2,000, an 80% chance of ending up with a value of $3,500, and a 10% chance of ending up with a value of $4,000?
a. $6,000
b. $3,500
c. $3,400
d. $3,250
e. $3,000

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values and $p_i$ are their corresponding probabilities.

Step2: Identify values and probabilities

We have $x_1 = 2000$, $p_1=0.1$; $x_2 = 3500$, $p_2 = 0.8$; $x_3=4000$, $p_3 = 0.1$.

Step3: Calculate the expected value

$E(X)=2000\times0.1 + 3500\times0.8+4000\times0.1$
$E(X)=200 + 2800+400$
$E(X)=3400$

Answer:

C. $\$3,400$