C: Expectation D: The Binomial Distribution 23CD

23C: EXPECTATION

TWO EXAMPLES:

23C: FAIR GAMES In gambling, we say the expected gain of the player from each game is the expected return or payout from the game, less the amount it cost them to play. The game will be fair if the expected gain is zero.

23C: ANOTHER EXAMPLE

23D: THE BINOMIAL DISTRIBUTION Special type of discrete random variable which is applied to sampling with replacement. The probability distribution that is associated with this variable is binomial probability distribution.

23D: BINOMIAL EXPERIMENTS

23D: EXAMPLE Suppose a spinner has three blue edges and one white edge. The chance of finishing on blue is ¾ and on white is ¼. If we call a blue result a “success” and white a “failure”, then we have a binomial experiment. WOW! Consider twirling the spinner n = 3 times. This is exciting. Find P(X = 0), P(X = 1), P(X = 2), and P(X = 3).

23D: EXAMPLE Suppose a spinner has three blue edges and one white edge. Consider twirling the spinner n = 3 times. This is still exciting. Find P(X = 0), P(X = 1), P(X = 2), and P(X = 3).

DID YOU NOTICE?

MORE FUN EXAMPLES FROM 23D

23D: THE BINOMIAL PROBABILITY DISTRIBUTION FUNCTION

EXAMPLE WITH CALCULATOR

EXAMPLE WITH CALCULATOR CONTINUED

23D: THE MEAN AND STANDARD DEVIATION OF A BINOMIAL DISTRIBUTION

23D: THE MEAN AND STANDARD DEVIATION OF A BINOMIAL DISTRIBUTION EXAMPLE