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"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

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)

Remember

Random variables are mathematical representations of random processes.

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