Question

rotter partners is planning a major investment. from experience, the amount of profit x (in millions of dollars) on a randomly selected invest- ment of this type is uncertain, but an estimate gives the following probability distribution:

Answer 1

To construct a probability distribution function (PDF) for each investment, we need to calculate the probability of each profit outcome and multiply it by the corresponding profit. The first investment has a PDF of $500,000, $300,000, and -$600,000. The second investment has a PDF of $600,000, $400,000, and -$400,000. The third investment has a PDF of $600,000, $0, and -$200,000.

Step-by-step explanation:

To construct a probability distribution function (PDF) for each investment, we need to determine the probability of each profit outcome and multiply it by the corresponding profit. Let's calculate the PDF for each investment:

First Investment:

• 10% chance of $5,000,000 profit: (0.1)(5,000,000) = $500,000
• 30% chance of $1,000,000 profit: (0.3)(1,000,000) = $300,000
• 60% chance of losing $1,000,000: (0.6)(-1,000,000) = -$600,000

Second Investment:

• 20% chance of $3,000,000 profit: (0.2)(3,000,000) = $600,000
• 40% chance of $1,000,000 profit: (0.4)(1,000,000) = $400,000
• 40% chance of losing $1,000,000: (0.4)(-1,000,000) = -$400,000

Third Investment:

• 10% chance of $6,000,000 profit: (0.1)(6,000,000) = $600,000
• 70% chance of no profit or loss: (0.7)(0) = $0
• 20% chance of losing $1,000,000: (0.2)(-1,000,000) = -$200,000

Answer 2

Rotter Partners is planning a major investment, and the estimated probability distribution of profits (in millions of dollars) is essential for decision-making.

Step-by-step explanation:

In probability distribution, each profit value is associated with a probability. By multiplying each profit by its probability and summing the results, we find the expected value. This calculation incorporates the uncertainty of profits, providing a more informed estimate for decision-makers.

The expected value acts as a central measure, reflecting the average profit Rotter Partners can expect based on the probability distribution. It serves as a valuable metric for decision-making, helping assess the potential outcome of the investment. In this context, understanding the expected value is crucial for evaluating the overall financial impact of the planned investment.

The probability distribution provides a comprehensive overview of potential profits and their likelihood. To obtain a final answer, calculate the expected value (E) of the profits. For each profit value, multiply it by its corresponding probability and sum the results. The formula for expected value is E(X) = Σ [x * P(x)], where x is the profit value and P(x) is its probability. This calculated expected value represents the average profit Rotter Partners can anticipate from the investment.