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# Chapter 17 & 18 Notes STAT 110 - 002

USC

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This 4 page Class Notes was uploaded by Kara Lyles on Saturday March 26, 2016. The Class Notes belongs to STAT 110 - 002 at University of South Carolina taught by Gail Ward-Besser (P) in Spring 2016. Since its upload, it has received 93 views. For similar materials see Introduction to Statistical Reasoning in Statistics at University of South Carolina.

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Date Created: 03/26/16

Chapter 18 Definitions Probability model- all possible outcomes Ex. If you toss a coin 3 times. What is the chance it lands on tails? (2^3=8) ANSWER: 8 Sample space - unique outcome Ex. When tossing a coin a unique outcome would be either heads or tails. Sample space= head (H) Tails (T) Event - collection of outcome Probability Rules Rule 1 : probability must be a number between 0 and 1 Rule 2: all possible outcome must = 1 *if it passes both rules 1&2 it’s legitimate Rule 3 AKA compliment rule: if the question ask what is the probability that the event doesn’t occur? Use this Formula: 1 - probability the event WILL Occur Probability = numerical (has to be a number) Ex. Probability of dog losing the race is .40, what is the probability of it winning? ANSWER: . 70 Complement = Opposite (think opposite) Ex. What is the compliment of the dog losing? ANSWER: The dog winning Rule 4: Union Rule, think united so there is addition. Probabilities must be disjoint. Formula: P (A or B) = P (A) +P (B) *There may be an instance where given 2 disjoint probabilities and then a probability of both occurring. If asked the probability of both occurring use this formula: P (A) + P (B) - P (A&B) Rule 5 Multiplication rule: If events are INDPENDENT of each other multiply. Sampling distribution- “Tells values a STATISTIC takes in repeated samples from the same population” **** Central Limit Theorem-the sampling distribution for the statistic is normally distributed when you take many, many samples of sufficiently large sample size (WILL BE ON TEST) Chapter 17 Definitions Random- individual outcomes uncertain but reaches random distribution over a lot of repetitions. Probability - # between 0&1 which describe the proportion of times an outcome will occur IF Probability =0 outcome never occurs IF probability = 1 outcome will occur every time IF probably = 1/2 outcome eventually happens half the time Types of Probabilities Empirical (experimental): experiment must take place YOU had to do something Theoretical: assumption Based on set theories Personal probability : personal judgement (you must believe it) Probability of an outcome= Number of ways for an outcome to occur / total number of outcomes. Law of large numbers: if numerical outcomes is repeated independently many times. * The mean of the observed outcomes will approach the expected value. Ex. Chance of getting heads or tails is 1/2. The more times you flip the coin the closer it will get to its expected value which is 1/2 Large of law numbers is about means and proportion. When speaking of odd assign A to the first probability and Assign B to the second one. If odds are for you use formula: A/ (A+B) If odds are against you use formula: B/ (A+B) If only given one probability use formula: O/ (1+O)

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