(2-1) $0\le P\left(\text{event}\right)\le 1$

A basic statement of probability.

(2-2) $P\left(A\text{ or }B\right)=P\left(A\right)+P\left(B\right)-P\left(A\text{ and }B\right)$

Probability of the union of two events.

(2-3) $P\left(A|B\right)=\frac{P\left(AB\right)}{P\left(B\right)}$

Conditional probability.

(2-4) $P\left(AB\right)=P\left(A|B\right)P\left(B\right)$

Probability of the intersection of two events.

(2-5) $P\left(A|B\right)=\frac{P\left(B|A\right)P\left(A\right)}{P\left(B|A\right)P\left(A\right)+P\left(B|A\prime \right)P\left(A\prime \right)}$

Bayes’ Theorem in general form.

(2-6) $E\left(X\right)={\displaystyle \sum _{i=1}^n}{X}_{i}P\left(X_i\right)$

An equation that computes the expected value (mean) of a discrete probability distribution.

(2-7) ${\sigma }^2=\text{Variance}={\displaystyle \sum _{i=1}^n}{\left[X_i-E\left(X\right)\right]}^{2}P\left(X_i\right)$

An equation that computes the variance of a discrete probability distribution.

(2-8) $\sigma =\sqrt{\text{Variance}}=\sqrt{{\sigma }^2}$

An equation that computes the standard deviation from the variance.

(2-9) Probability of r successes in n trials

$=\frac{n!}{r!\left(n-r\right)!}{p}^r{q}^{n-r}$

A formula that computes probabilities for the binomial probability distribution.

(2-10) $\text{Expected value }\left(\text{mean}\right)=np$

The expected value of the binomial distribution.

(2-11) $\text{Variance}=np\left(1-p\right)$

The variance of the binomial distribution.

(2-12) $f\left(X\right)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{}\frac{{}^{\mathrm{-}{\left(x-\mu \right)}^2}}{{}^{2{\sigma }^2}}$

The density function for the normal probability distribution.

(2-13) $Z=\frac{X-\mu }{\sigma }$

An equation that computes the number of standard deviations, Z, the point X is from the mean $\mu .$

(2-14) $f\left(X\right)=\mu e^{\mathrm{-}\mu x}$

The exponential distribution.

(2-15) $\text{Expected value}=\frac{1}{\mu }$

The expected value of an exponential distribution.

(2-16) $\text{Variance}=\frac{1}{{\mu }^2}$

The variance of an exponential distribution.

(2-17) $P\left(X\le t\right)=1-e^{\mathrm{-}\mu t}$

Formula to find the probability that an exponential random variable, X, is less than or equal to time t.

(2-18) $P\left(X\right)=\frac{{\lambda }^x{e}^{\mathrm{-}\lambda }}{X!}$

The Poisson distribution.

(2-19) $\text{Expected value}=\lambda$

The mean of a Poisson distribution.

(2-20) $\text{Variance}=\lambda$

The variance of a Poisson distribution.