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§6-3

§6-3. Binomial & Geometric Random Variables. 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. What do these have in common?.

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§6-3

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  1. §6-3 Binomial & Geometric Random Variables

  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 • 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. • Choose three students at random from your class. Let Y = the # who are over 6 feet tall. • 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

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