Chapter 6Formulas and Vocabulary

• Continuous random variable (p. 311)
• Discrete random variable (p. 311)
• Expected value, or expectation, of a random variable $X$ (p. 318). Denoted as $E$($X$).
• Mean $\mu$ of a discrete random variable (p. 315).
  $\mu =\Sigma [X\cdot P(X\left)\right]$
• Probability distribution of a discrete random variable (p. 312)
• Random variable (p. 310)
• Rules for a discrete probability distribution (p. 313).
  $\Sigma P\left(X\right)=1$ and $0\le P\left(X\right)\le 1$

• Variance and standard deviation of a discrete random variable (p. 319).

  $\begin{array}{c}\text{Variance}:{\sigma }^2={\displaystyle \sum [{(X-\mu )}^2\cdot P(X\left)\right]}\\ \text{Standard deviation}:\sigma =\sqrt{{\displaystyle \sum [{(X-\mu )}^2\cdot P(X\left)\right]}}\end{array}$

• Binomial experiment (p. 327)
• Binomial probability distribution formula (p. 330).
  $P\left(X\right)={(}_n{C}_x)p^x{(1-p)}^{n-X}$
• Factorial (!) (p. 329). $n!\; =n(n-1)(n-2)\dots (2)(1)$
• Mean, variance, and standard deviation of a binomial random variable $X$ (p. 334).

  Mean (or expected value): $\mu =n\cdot p$

  Variance: ${\sigma }^2=n\cdot p\cdot (1-p)$

  Standard deviation: $\sigma =\sqrt{n\cdot p\cdot (1-p)}$

• Number of combinations (p. 329).

  ${}_n{C}_x=\frac{n!}{X!(n-X)!}$

• Mean, variance, and standard deviation for a Poisson random variable (p. 344). Mean = $\mu$, Variance = ${\sigma }^2=\mu$, $\text{standard deviation}=\sigma =\sqrt{\mu }$.

• Poisson probability distribution formula (p. 342).

  $P\left(X\right)=\frac{{\mu }^x\cdot e^{-\mu }}{X!}$

• Continuous probability distribution (p. 349)
• Density curve (p. 349)
• Law of Total Probability for Continuous Random Variables (p. 349)
• Probability for continuous distributions (p. 350)
• Properties of the normal density curve (normal curve) (p. 352)
• Requirements for a continuous probability distribution (p. 349)
• Uniform probability distribution (p. 349)
• Standard normal ($Z$) distribution (p. 354)
• $Z$ table for the standard normal random variable $Z$ (p. 355)

• Finding normal data values for specified probabilities (p. 372)
• Finding probabilities for any normal distribution (p. 369)

• Standardizing a normal random variable (p. 368).

  $Z=\frac{X-\mu }{\sigma }$

• Normal probability plot (p. 379)

• Normal approximation to the binomial probability distribution (p. 386)