CH+10 - Introducing probability BPS chapter 10 2006 W. H....

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Introducing probability BPS chapter 10 © 2006 W. H. Freeman and Company
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Objectives (BPS chapter 10) Introducing probability The idea of probability Probability models Probability rules Discrete sample space Continuous sample space Random variables Personal probability
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A phenomenon is random if individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions. Randomness and probability The probability of any outcome of a random phenomenon can be defined as the proportion of times the outcome would occur in a very long series of repetitions.
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Coin toss The result of any single coin toss is random. But the result over many tosses is predictable, as long as the trials are independent (i.e., the outcome of a new coin toss is not influenced by the result of the previous toss). First series of tosses Second series The probability of heads is 0.5 = the proportion of times you get heads in many repeated trials.
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The trials are independent only when you put the coin back each time. It is called sampling with replacement. Two events are independent if the probability that one event occurs on any given trial of an experiment is not affected or changed by the occurrence of the other event. When are trials not independent? Imagine that these coins were spread out so that half were heads up and half were tails up. Close your eyes and pick one. The probability of it being heads is 0.5. However, if you don’t put it back in the pile, the probability of picking up another coin and having it be heads is now less than 0.5.
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Probability models mathematically describe the outcome of random processes. They consist of two parts: 1) S = Sample Space: This is a set, or list, of all possible outcomes of a random process. An event is a subset of the sample space. 2) A probability for each possible event in the sample space S. Probability models Example: Probability Model for a Coin Toss S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5
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Important: It’s the question that determines the sample space. Sample space A. A basketball player shoots three free throws. What are the possible sequences of hits (H) and misses (M)? H H H - HHH M M M - HHM H - HMH M - HMM S = {HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM } Note: 8 elements, 2 3 B. A basketball player shoots three free throws. What is the number of baskets made? S = {0, 1, 2, 3} C. A nutrition researcher feeds a new diet to a young male white rat. What are the possible outcomes of weight gain (in grams)? S = [0, ] = (all numbers ≥ 0)
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Coin Toss Example: S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5 1) Probabilities range from 0 ( no chance of the event ) to 1 ( the event has to happen ).
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CH+10 - Introducing probability BPS chapter 10 2006 W. H....

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