Statistics & Probability / TERMS L01-L07

Variable

– is the characteristic or property of the element.

Random variable

is a variable being measured to produce numerical observations associated with the random outcomes of a chance experiment.

Random variable

is a function whose domain is the sample space of a random experiment, and the range of the random variable is the smallest interval that contains all the values of the random variable.

Random variable

it is typically represented by an uppercase letter, usually X, while its corresponding lowercase letter in this case, x, is used to represent one of its values.

Sample space

– is the set of all possible outcomes of an experiment

Event

– outcomes of an experiment

Discrete and Continuous Random Variable

Two types of Random Variables:

Discrete random variable

– a random variable that can assume at most a finite or a countable number of possible values.

Example: The random variable X is the sum of the spots on two dice is __________ since x can assume only the values 2,3,4,5,6,7,8,9,10,11 and 12.

The number of possible outcomes is finite or can be counted.

Continuous random variable

– is one that can assume any value in some interval or intervals of real numbers, and the probability that it assumes any specific value is greater than zero. This random variable has no gaps

example: height of individuals, time taken to complete a task.

Discrete Random Variable

• is a random variable whose set of all possible values are countable or infinitely countable.

• is a random variable where the observed numerical value is produced by counting and assumes whole number values.

Continuous Random Variable

• a random variable whose set of all possible values are not countable

• assumes an infinite number of values in an interval between two specific values. This means they can assume values that can be represented by fractions and decimals.

• has values often resulting from measurements.

Statistics

• is used to validate or test a claim or inference about a group of people or object or a series of events. It helps people answer questions and make decisions about many things.

probability value

• is the ratio of the frequency of occurrences relative to the total number of occurrences.

Mean

• central value or average of the corresponding probabilty mass function

• Measure of central tendency or location

• also called the expected Value

mean of a discrete variable

this formula can be used in finding the _____

Variance

• denoted as σ², is determined by using the formula:

Standard Deviation

• denoted as σ, is the square root of the variance and this formula: