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Chapter 2__Probability
Chapter 2__Probability

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Probability Probability: A measure of the chance that something will

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Computer Science 341 Discrete Mathematics Homework 11

... Let R be the number of runs in n independent tosses of a biased coin. (Runs are consecutive tosses with the same result). Each coin toss is a head (H) with probability p and is a tail (T) with probability 1 − p. Show that the variance of R is at most 4n · p(1 − p). (Hint: Let X i be an indicator var ...
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Survey of Math: Chapter 7: Probability (Lecture 1) Page 1 The result

... was the same. Since the text dealt with fair dice, they did not include Rule 5 in their list. We used Rule 5 when we said the roll of the two dice, although done at the same time, were independent events. Rule 5 is also useful when events are performed in sequence, since then the events are independ ...
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Stats Probability and statistical hypothesis testing

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Chapter 4 – Probability

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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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