(3-1) $\text{EMV}\left(\text{alternative} i\right)={\displaystyle \sum _{}^{}}{X}_{i}P\left(X_i\right)$

An equation that computes expected monetary value.

(3-2) $\begin{array}{lll}\text{EVwPI}\hfill & =\hfill & \Sigma \text{(Best payoff in state of nature }i\text{)}\hfill \\ \hfill & \hfill & \times \text{ (Probability of state of nature }i\text{)}\hfill \end{array}$

An equation that computes the expected value with perfect information.

(3-3) $\text{EVPI}=\text{EVwPI}-\text{Best} \text{EMV}$

An equation that computes the expected value of perfect information.

(3-4) $\text{EVSI}=\left(\text{EV} \text{with} \text{SI}+\text{cost}\right)-\left(\text{EV} \text{without} \text{SI}\right)$

An equation that computes the expected value (EV) of sample information (SI).

(3-5) $\text{Efficiency} \text{of} \text{sample} \text{information}=\frac{\text{EVSI}}{\text{EVPI}}100\%$

An equation that compares sample information to perfect information.

(3-6) $P\left(A|B\right)=\frac{P\left(B|A\right)P\left(A\right)}{P\left(B|A\right)P\left(A\right)+P\left(B|A\prime \right)P\left(A\prime \right)}$

Bayes’ Theorem—the conditional probability of event A given that event B has occurred.

(3-7) $\text{Utility} \text{of} \text{other} \text{outcome}=\left(p\right)\left(1\right)+\left(1-p\right)\left(0\right)=p$

An equation that determines the utility of an intermediate outcome.