Discrete Distribution (Lucky Dice Experiment) Quiz

PDF page 283: • The student will compare empirical data and a theoretical distribution to determine if a Tet gambling game fits a

PDF page 283: The number of matches will decide your profit.

PDF page 283: Round answers to relative frequency and probability problems to four decimal places.

PDF page 283: • The student will demonstrate an understanding of long-term probabilities.

PDF page 286: Binomial Probability Distribution a discrete random variable (RV) that arises from Bernoulli trials; there are a fixed number, n, of independent trials. “Independent” means that the result of any trial (for example, trial one) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X ~ B(n, p). The

PDF page 286: mean is μ = np and the standard deviation is σ = npq . The probability of exactly x successes in n trials is

PDF page 288: The outcomes of a binomial experiment fit a binomial probability distribution. The random variable X = the number of successes obtained in the n independent trials. The mean of X can be calculated using the formula μ = np, and the standard

PDF page 286: Geometric Distribution a discrete random variable (RV) that arises from the Bernoulli trials; the trials are repeated until the first success. The geometric variable X is defined as the number of trials until the first success. Notation: X ⎞ 1 1⎛1

PDF page 288: In a geometric experiment, define the discrete random variable X as the number of independent trials until the first success. We say that X has a geometric distribution and write X ~ G(p) where p is the probability of success in a single trial.

PDF page 288: In a geometric experiment, define the discrete random variable X as the number of independent trials until the first success. We say that X has a geometric distribution and write X ~ G(p) where p is the probability of success in a single trial.

PDF page 289: X ~ G(p) means that the discrete random variable X has a geometric probability distribution with probability of success in a single trial p. X = the number of independent trials until the first success X takes on the values x = 1, 2, 3, ... p = the probability of a success for any trial

PDF page 286: We sample from two groups of items when we are interested in only one group. X is defined as the number of successes out of the total number of items chosen. Notation: X ~ H(r, b, n), where r = the number of items in the group of interest, b = the number of items in the group not of interest, and n = the number of items chosen.

PDF page 288: The outcomes of a hypergeometric experiment fit a hypergeometric probability distribution. The random variable X = the number of items from the group of interest. The distribution of X is denoted X ~ H(r, b, n), where r = the size of the group of interest (first group), b = the size of the second group, and n = the size of the chosen sample. It follows that rbn(r + b − n) nr

PDF page 289: X ~ P(μ) means that X has a Poisson probability distribution where X = the number of occurrences in the interval of interest. X takes on the values x = 0, 1, 2, 3, ... The mean μ is typically given.

PDF page 287: The distribution is defined by the mean μ of the event in the interval. Notation: X ~ P(μ). The mean is μ = np. The

PDF page 289: The variance is σ = μ, and the standard deviation is

PDF page 287: x! The Poisson distribution is often used to approximate the binomial distribution, when n is “large” and p is “small” (a general rule is that n should be greater than or equal to 20 and p should be less than or equal to 0.05). Probability Distribution Function (PDF) a mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome. Random Variable (RV) a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters X, Y, Z,...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters x, y, and z. For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3,.... Variables in statistics differ from variables in intermediate algebra in the two following ways.

PDF page 288: A Poisson probability distribution of a discrete random variable gives the probability of a number of events occurring in a fixed interval of time or space, if these events happen at a known average rate and independently of the time since the last event. The Poisson distribution may be used to approximate the binomial, if the probability of success is "small" (less than or equal to 0.05) and the number of trials is "large" (greater than or equal to 20).