Section 7.1Discrete and Continuous Random VariablesAP Statistics

AP Statistics, Section 7.1, Part 1 2

Random Variables

A random variable is a variable whose value is a numerical outcome of a random phenomenon.

For example: Flip three coins and let X represent the number of heads. X is a random variable.

We usually use capital letters to denotes random variables.

AP Statistics, Section 7.1, Part 1 3

Random Variables

A random variable is a variable whose value is a numerical outcome of a random phenomenon.

For example: Flip three coins and let X represent the number of heads. X is a random variable.

The sample space S lists the possible values of the random variable X

AP Statistics, Section 7.1, Part 1 4

Discrete Random Variable

A discrete random variable X has a countable number of possible values.

For example: Flip three coins and let X represent the number of heads. X is a discrete random variable.

We can use a table to show the probability distribution of a discrete random variable.

AP Statistics, Section 7.1, Part 1 5

Discrete Probability Distribution Table

Value of X: x1 x2 x3 … xn

Probability:p1 p2 p3 … pn

AP Statistics, Section 7.1, Part 1 6

Probability Distribution Table: Number of Heads Flipping 4 Coins

TTTT

TTTHTTHTTHTTHTTT

TTHHTHTHHTTHHTHTTHHTHHTT

THHHHTHHHHTHHHHT

HHHH

X 0 1 2 3 4

P(X) 1/16 4/16 6/16 4/16 1/16

AP Statistics, Section 7.1, Part 1 7

Discrete Probability Distributions Can also be shown using a histogram

AP Statistics, Section 7.1, Part 1 8

AP Statistics, Section 7.1, Part 1 9

What is the average number of heads?

61 4 4 116 16 16 16 16

0 4 12 12 416 16 16 16 16

3216

0 1 2 3 4

2

x

AP Statistics, Section 7.1, Part 1 10

AP Statistics, Section 7.1, Part 1 11

Continuous Random Variable

A continuous random variable X takes all values in an interval of numbers.

AP Statistics, Section 7.1, Part 1 12

Distribution of Continuous Random Variable

AP Statistics, Section 7.1, Part 1 13

Distribution of Continuous Random Variable The probability distribution of X is

described by a density curve. The probability of any event is the area

under the density curve and above the values of X that make up that event.

AP Statistics, Section 7.1, Part 1 14

Normal distributions as probability distributions Suppose X has N(μ,σ) then we can use

our tools to calculate probabilities.