Chapter 4 Random Variable and Probability Distribution

standard normal distribution

a normal distribution with mu = 0 and SD - 1. A random variable with a standard normal distribution, denoted by Z is called a standard normal random variable

normal probability plot

a scatterplot with the ranked data values on one axis and their corresponding Z scores on the other.

random variable

a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point.

uniform probability distribution

continuous random variables that appear to have equally likely outcomes over their range of possible values

binomial random variable

doing an experiment for a fixed number n of times and observing the number x of times that one of the two possible outcomes occur.

uniform frequency function

has a rectangular shape.

exponential random variables

have to find areas under exponential probability distribution

probability distribution

of a discrete random variable: a graph, table, or formula that specifies the probability associated with each possible value the random variable can assume.

randomness distribution

one way of generating a uniform random variable is to perform an experiment in which a point is randomly selected on a horizontal axis between points c and d.

hypergeometric probability distribution

provides a realistic model for some types of enumerative (countable) data.

discrete

random variables that can assume a countable number (finite or infinite) of values

continuous

random variables that can assume values corresponding to any of the points contained in one or more intervals (i.e. values that are infinite and uncountable)

poisson distribution

type of discrete probability distribution that is often useful in describing the number of rare events that will occur in a specific period of time or in a specific area or volume.

correction for continuity

we are correcting the discrete distribution so that it can be approximated by the continuous one.

probability distribution for a continuous random variable

x, can be represented by a smooth curve- a function of x, denoted f(x). The probability that x falls between two values, a and b, is the area under the curve between a and b.