PART III SUMMARY

Here are the most important skills you should have acquired after reading Chapters 17 through 20.

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  1. A. RANDOMNESS AND PROBABILITY

    1. 1. Recognize that some phenomena are random. Probability describes the long-run regularity of random phenomena.

    2. 2. Understand the idea of the probability of an event as the proportion of times the event occurs in very many repetitions of a random phenomenon. Use the idea of probability as long-run proportion to think about probability.

    3. 3. Recognize that short runs of random phenomena do not display the regularity described by probability. Understand that randomness is unpredictable in the short run. Avoid seeking causal explanations for random occurrences.

  2. B. PROBABILITY MODELS

    1. 1. Use basic probability facts to detect illegitimate assignments of probability: any probability must be a number between 0 and 1, and the total probability assigned to all possible outcomes must be 1.

    2. 2. Use basic probability facts to find the probabilities of events that are formed from other events: the probability that an event does not occur is 1 minus its probability. If two events cannot occur at the same time, the probability that one or the other occurs is the sum of their individual probabilities.

    3. 3. When probabilities are assigned to individual outcomes, find the probability of an event by adding the probabilities of the outcomes that make it up.

    4. 4. When probabilities are assigned by a Normal curve, find the probability of an event by finding an area under the curve.

  3. C. EXPECTED VALUE

    1. 1. Understand the idea of expected value as the average of numerical outcomes in very many repetitions of a random phenomenon.

    2. 2. Find the expected value from a probability model that lists all outcomes and their probabilities (when the outcomes are numerical).

  4. D. SIMULATION

    1. 1. Specify simple probability models that assign probabilities to each of several stages when the stages are independent of each other.

    2. 2. Assign random digits to simulate such models.

    3. 3. Estimate either a probability or an expected value by repeating a simulation many times.