Discrete and Continuous Probability Distributions

Parameters

________- key pieces of identifying information for distributions.

outcome of interest

The ________ is referred to as a success.

Random variable

a function that assigns a number to each possible outcome in a random experiment

Discrete random variables

when modeling the behavior of a discrete random variable, we use a discrete probability function that can usually be expressed by a formula or table

Continuous random variables

when modeling the behavior of a continuous random variable, we use a continuous probability function that takes form of a curve

Properties

the entire curve must be above the x-axis and the total area underneath the curve must be 1

Finding probabilities

we find the area under the curve between the two endpoints of the interval

Conditions of binomial distributions:

Fixed number of trials

Two possible outcomes (success or failure)

The probability of success, p, is the same for each trial

Trials are independent (the outcome of one trial does not affect other trials)

Parameters

key pieces of identifying information for distributions

The shape of the binomial distribution depends on

the number of trials (n) and the probability of success (p)

Normal distribution parameters

Mean

Standard deviation