IPS6eCh04_1and4_2bb

IPS6eCh04_1and4_2bb - Probability: The Study of Randomness...

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    Probability: The Study of  Randomness Randomness and Probability Models IPS Chapters 4.1 and 4.2
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Objectives (IPS Chapters 4.1 and 4.2) Randomness and Probability models Probability and Randomness Sample spaces Probability rules Assigning probabilities: finite number of outcomes Assigning probabilities: equally likely outcomes Independence and multiplication rule
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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 flip is not influenced by the result of the previous flip). 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 that is heads up is now less than 0.5.
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Probability models describe, mathematically, the outcome of random processes. They consist of two parts: 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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A. A basketball player shoots three free throws. What are the possible sequences of hits (H) and misses (M)? H
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IPS6eCh04_1and4_2bb - Probability: The Study of Randomness...

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