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7.1 Random Variables
7.1 Random Variables

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Lesson 7.1

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Law of Multiplication - Books in the Mathematical Sciences

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... as safe as Des Moines? Explain why or why not. There are many acceptable answers, depending on your interpretation. Here is a great answer from Dr. Hofmann. In order to make a comparison between Chicago or DSM, we will have to adjust rates to the same units - i.e. we could for example look at homici ...
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... A coin is tossed. If “Head” turns up a ball is drawn from Box 1, and if “Tail” turns up then a ball is drawn from Box 2. Find the probability of selecting a red ball. P(H and Red) + P(T and Red) = P(H)P(Red|H) + P(T)P(Red|T) ...
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... Two events are dependent if the probability of them occurring is affected by the other occurring. For example, if I drew from a deck of cards an Ace, then probability drawing another Ace from the deck (without replacing the first card) would be affected by drawing the first Ace. P(E and F) This lead ...
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... Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one ...
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Module 5: Decision Theory

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... that a player wins the small prize? Solution: If exactly three digits are matched, one of the four digits must be incorrect and the other three digits must be correct. For the digit that is incorrect, there are 9 possible choices (all except the correct digit). The digit that is incorrect can be in ...
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... • no statistic or statistical test can make practical decision • whether one risks being wrong cautiously (type I) or wrong incautiously (type II) cannot be decided absent cost and risk, what’s at stake, needs etc • no statistical analysis better than the numbers (descriptions) fed into it: garbage ...
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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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