select the correct answer.\nwhat is the expected value of an original investment of $3,000 that has a 10%…

select the correct answer.\nwhat 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?\n\na. $6,000\nb. $3,500\nc. $3,400\nd. $3,250\ne. $3,000

select the correct answer.\nwhat 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?\n\na. $6,000\nb. $3,500\nc. $3,400\nd. $3,250\ne. $3,000

Answer

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

$E(X)=x_1p_1 + x_2p_2+x_3p_3=2000\times0.1+3500\times0.8 + 4000\times0.1$ $=200 + 2800+400$ $=3400$

Answer:

C. $3,400$