AP Statistics Audio Lectures

Random Variables

by Arnold Kling

Random Variables

by Arnold Kling

To hear the lecture, click here.

"Random Variable" is a mathematical representation of a random process. Analogous to a circle or a triangle geometry

Random variables assign numbers and probabilities to outcomes of random processes; examples:

- the sum of two dice, and the probability of getting each particular sum

...X P(X) 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 - pick a card at random from a deck, and assign a value of 4 points to an ace, 3 points to a king, 2 points to a queen and 1 point from a jack.
X P(X) 4 1/13 3 1/13 2 1/13 1 1/13 0 9/13 - pick a family at random from zip code 20902, and count the number of children

...X P(X) 10 0 9 .005 8 .012 7 .015 6 .027

Random Variables can be Continuous

- rainfall in October in Silver Spring
- height in centimeters of a pine tree in a forest

think of X as the midpoint of a range, and p(X) as the probability that the random variable will fall within that range

Random Variable Represented as a Histogram

Random Variable and Gambling

A lottery that costs $1, has 10,000 entrants, a grand prize of $5000 and four smaller prizes of $100 each

X | P(X) |
---|---|

+ $4999 | 1/10,000 |

+ $99 | 4/10,000 |

- $1 | 9,995/10,000 |

Many mathematical models of random variables (many shapes in geometry)

Two used in this course: binomial; normal (bell curve)

Two others mentioned briefly: geometric; uniform (rectangular)

Random variables are mathematical representations of random processes.

We assign a number to each outcome and associate a probability with that number.