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Total Cost:

Total Revenue:

Total Profit: Break-even Point:

Where:

Example:

Probability and Statistics:

P(A or B) = P(A) + P(B) – P(AB)

Where

P(A or B) = probability event A or B or both will occur, P(A) = probability event A will occur, P(B) = probability event B will occur, P(AB) = probability that both event A and B will occur. Example:

P(Negative Test Result or Not Pregnant) = P(Negative Test Result) + P(Not Pregnant) – P(Negative Test Result and Not Pregnant) = 16/99 + 14/99 – 11/99 = 19/99

Independent Events:

A succession of events that do not affect each other.

If A and B are independent, P(AB) = P(A)•P(B)

Example:

Flip a coin twice, the probability of a head followed by a tail is:

P(HT) = P(H)•P(T) = (.5)(.5) = .25

Binomial Distribution: Example:

Assume n= 20, p=0.1

P(r ≥ 5) – rejected.

P(r < 5) – accepted.

P(r < 5) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3) + P(r = 4)

P(r < 5) = P(r < 5) = 0.1216 + 0.2702 + 0.2852 + 0.1901 + 0.0898 = 0.9569 (accepted)

P(r ≥ 5) = 1 – P(r < 5) = 1 – 0.9569 = 0.0431 (rejected)

Expected Value:

E(x) =

Example: x P(x) x•P(x)

0 .10 0

1 .20 .20

2 .30 .60

3 .25 .75

4 .15 .60 ∑x•P(x) = 2.15

Normal Distribution:

Example:

Note: x = 400 is to the left of the mean in following example.

Note: x = 19 is to the right of the mean in the following example.

Decision Analysis:

Maximax: First select the maximum payoff of each decision, then select the maximum of those.

Maximin: First select the minimum payoff for each decision, then select the maximum of those.

Minimax Regret: First select the maximum payoff under each state of nature. All other payoffs under the respective states of nature are subtracted from these amounts. Select the maximum regret for each decision. The decision corresponding to the minimum of these regret values is then selected.

Hurwicz: For each decision, multiply the best payoff by alpha, and the worst payoff by (1-alpha). The best result is selected.

Equal Likelihood: For each decision, multiply the decision payoff for each state of nature by an equal weight, where the sum of the weights is equal to one. Select the best value.

States of Nature having Probabilities: Compute the expected value for each decision by by multiplying each decision outcome under each state of nature by the probability of its occurrence. Select the best expected value.

Example:…...

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