1. Binomial & Geometric Random Variables §6-3

2. Goals: Binomial settings and binomial random variables Binomial probabilities Mean and standard deviation of a binomial distribution Binomial distributions in statistical sampling Geometric random variables

3. What do these have in common? Toss a coin 5 times. Count the # of heads. Spin a roulette wheel 8 times. Record how many time the ball lands in a red slot Take a random sample of 100 babies born in the US today. Count the number of little girls.  Repeated trials of the same chance process  # of trials is fixed in advance  Trials are independent  Looking for a # of successes  Chance of success is the same for each trial

4. BS…Binomial Setting When these conditions are meet we have a binomial setting. Definition A binomial setting arises when we perform several independent trials of the same chance process and record the number of items that a particular outcome occurs. The 4 conditions for a binomial setting are Binary? Independent? Number? Success? BINS

5. “BINS” Binary…possible outcomes can be classified as a “success” or “failure” Independent…the result of one trial cannot have an effect on another trial Number…the # of trials, n, is fixed in advance Success…probability of success on each trial is the same

6. Binomial random variable & binomial distribution The count X of successes in a binomial setting is a binomial random variable. The probability distribution of X is a binomial distribution with parameters n and p, where n is the # of trials of the chance process and p is the probability of a success on any one trial. The possible values of X are the whole numbers from 0 to n.

7. Examples Type O blood…. Turn over 10 cards record aces… Turn over top card, replace, repeat until …

8. More examples 1. Shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process 10 times. Let X = the # of aces you observe. 2. Choose three students at random from your class. Let Y = the # who are over 6 feet tall. 3. Flip a coin. If it’s heads, roll a 6-sided die. If it’s tails, roll and 8-sided die. Repeat this process 5 times. Let W = the # of 5’s you roll.

9. Homework Page 403 69-73 all