Question

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(O_j) whose outcomes were uncertain would be calculated as: n

E(O_j) = P(q_i) O_ij

I = 1

where:

n

E(O_j) is the sum of the subjective or personal probabilities, P(q_i) for

I = 1

each event-action combination O_ij 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?

Answer 1

Given data available for the maize yield for the estimation of current year yield:

For the best season of 1 year out of 10, a farmer believes the yield of maize could be 6 tonnes

tonnes per hectare. For a good season, the yield could be 5.5 tones per hectare for 3 years out of 10. For the most likely season, the yield could be 5 tonnes

tonnes per hectare in 4 years out of 10. For a poor season, the yield could be 1 tonnes

tonnes per hectare in 1 year out of 10. For the very worst season, the yield could be 0.5 tonnes

tonnes per hectare in 1 year out of 10.

Now for the probability calculations for last 10 years as below:

1. For the best season         :  6 tonnes per hectare  for 1 year out of 10 years.

2. For a good season           :  5.5 tonnes per hectare for 3 years out of 10

 years.    

3. For the most likly season:  5 tonnes per hectare for 4 years out of 10 years.

4. For a poor season            :  1 tonnes per hectare for 1 year out of 10 years.

5. For the very worst season: 0.5 tonnes per hectare for 1 year out of 10

 years.

Now, check the complete data set for the timeline provided in the statement as

 10 years.

So

               $1+3+4+1+1=10$

This implies that, we have the complete data of last 10 years to come with the

 estimation.

 By using the estimation formula:

    Expected yield for the maize

$=6×\frac{1}{10}+5.5×\frac{3}{10}+5×\frac{4}{10}+1×\frac{1}{10}+0.5×\frac {1}{10}\\ =0.6+1.65+2+0.1+0.05 \\ =4.4$

Hence, The expected yield for the maize is 4.4 tonnes per hectare.