Probability Distributions
Introduction
Learning objectives for this lesson
Upon completion of this lesson, you should be able to:
distinguish between discrete and continuous random variables
explain the difference between population, parameter, sample, and statistic
determine if a given value represents a population parameter or sample statistic
find probabilities associated with a discrete probability distribution
compute the mean and variance of a discrete probability distribution
find probabilities associated with a binomial distribution
find probabilities associated with a normal probability distribution using the standard normal table
determine the standard error for the sample proportion and sample mean
apply the Central Limit Theorem properly to a set of continuous data
Random Variables
A
random variable
is numerical characteristic of each event in a sample space, or equivalently, each individual in a population.
Examples:
The number of heads in four flips of a coin (a numerical property of each different sequence of flips).
Heights of individuals in a large population.
Random variables are classified into two broad types
A
discrete random variable
has a countable set of distinct possible values.
A
continuous random variable
is such that any value (to any number of decimal places) within some interval is a possible value.
Examples of discrete random variable:
Number of heads in 4 flips of a coin (possible outcomes are 0, 1, 2, 3, 4).
Number of classes missed last week (possible outcomes are 0, 1, 2, 3, ..., up to some maximum number)
Amount won or lost when betting $1 on the Pennsylvania Daily number lottery
Examples of continuous random variables:
Heights of individuals
Probability Distributions
http://onlinecourses.science.psu.edu/stat200/book/export/html/34
1 of 17
9/27/2010 11:48 PM
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Time to finish a test
Hours spent exercising last week.
Note
: In practice, we don't measure accurately enough to truly see all possible values of a continuous random variable. For instance, in reality somebody may
have exercised 4.2341567 hours last week but they probably would round off to 4. Nevertheless, hours of exercise last week is inherently a continuous random
variable.
Probability Distributions: Discrete Random Variables
For a discrete random variable, its
probability distribution
(also called the probability distribution function) is any table, graph, or formula that gives each
possible value and the probability of that value.
Note
: The total of all probabilities across the distribution must be 1, and each individual probability must be
between 0 and 1, inclusive.
Examples:
(1) Probability Distribution for Number of Heads in 4 Flips of a coin
Heads
0
1
2
3
4
Probability
1/16
4/16
6/16
4/16
1/16
This could be found be listing all 16 possible sequences of heads and tails for four flips, and then counting how many sequences there are for each possible
number of heads.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 BARROSO,JOAOR
 Statistics, Normal Distribution, Probability, Probability distribution, Probability theory

Click to edit the document details