SOLUTION: a. Professors M. Boehlje and V. Eidman in their book Farm Management described a way that in budgeting, probabilities can be used to calculate expected values for uncertain variabl

Question 1184196: a. Professors M. Boehlje and V. Eidman in their book Farm Management described a way that in budgeting, probabilities can be used to calculate expected values for uncertain variables such as crop yields and prices for output.
A farmer at the beginning of the year is going to use the calculation of probabilities for determining an expected value for the yield of a crop of Maize.
The expected value of a project E(Oj) whose outcomes were uncertain would be calculated as: n
E(Oj) = P(qi) Oij
I = 1
where:
n
E(Oj) is the sum of the subjective or personal probabilities, P(qi) for
I = 1
each event-action combination Oij occurring.
For the best season of 1 year out of 10, a farmer believes the yield of wheat could be 5 tonnes per hectare.
For a good season, the yield could be 4 tonnes per hectare for 3 years out of 10.
For the most likely season, the yield could be 3 tonnes per hectare in 4 years out of 10.
For a poor season, the yield could be 1 tonne per hectare in 1 year out of 10.
For the very worst season, the yield could be 0.5 tonnes per hectare in 1 year out of 10.
Calculate the expected yield for wheat that would be used in the budget. (20 marks)

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the expected yield of wheat using the provided probabilities:
1. **Identify the Possible Outcomes (Oij) and their Probabilities (P(qi)):**
| Season | Yield (Tonnes/Hectare) (Oij) | Number of Years | Probability P(qi) |
|---------------|---------------------------|-----------------|-----------------|
| Best | 5 | 1 | 1/10 = 0.1 |
| Good | 4 | 3 | 3/10 = 0.3 |
| Most Likely | 3 | 4 | 4/10 = 0.4 |
| Poor | 1 | 1 | 1/10 = 0.1 |
| Very Worst | 0.5 | 1 | 1/10 = 0.1 |
2. **Calculate the Expected Value E(Oj):**
Use the formula: E(Oj) = Σ [P(qi) * Oij]
E(Oj) = (0.1 * 5) + (0.3 * 4) + (0.4 * 3) + (0.1 * 1) + (0.1 * 0.5)
E(Oj) = 0.5 + 1.2 + 1.2 + 0.1 + 0.05
E(Oj) = 3.05
Therefore, the expected yield for wheat that would be used in the budget is 3.05 tonnes per hectare.

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