Question

the triple l investment club is considering purchasing a certain stock. after considerable research, the club members determine that there is a 40% chance of making $13,000, a 20% chance of breaking even, and a 40% chance of losing $6,800. find the expectation of this purchase. the expected value is $

Explanation:

Step1: Recall the formula for expected value

The formula for expected value \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) is the outcome and \(p_i\) is the probability of that outcome.

Step2: Assign values to \(x_i\) and \(p_i\)

Let \(x_1 = 13000\), \(p_1=0.4\); \(x_2 = 0\) (breaking - even means no gain or loss), \(p_2 = 0.2\); \(x_3=-6800\) (negative because it's a loss), \(p_3 = 0.4\).

Step3: Calculate each term \(x_ip_i\)

• For the first term: \(x_1p_1=13000\times0.4 = 5200\)
• For the second term: \(x_2p_2=0\times0.2=0\)
• For the third term: \(x_3p_3=-6800\times0.4=-2720\)

Step4: Sum up the terms

\(E(X)=5200 + 0+(-2720)\)

Answer:

\(2480\)