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Exercise 4
Exercise 4

... 5. Thirty percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. (a) Let X= the number of the six customers who will make a purchase. Write the binomial formula for this situation. (b) Wh ...
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... • Bayes’ formula is relevant if we know that E occurred and we want to know which of the F’s occurred. P  Fj | E   ...
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Unit 4 Summary : Probability (Part 1)

... 5. How to modify a sample space to an altered sample space for conditional probability: P(rolling 3 | rolling odd) --> the sample space was originally {1, 2, 3, 4, 5, 6} but the alterned sample space is {1, 3, 5}. 6. How to use tree diagrams to solve probabilities. 7. How to use the "And" formula to ...
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STATISTICAL METHOD 1

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... The course is intended for the 1st year students of the PhD programme in Economics. The purposes of this course are: (i) to explain, at an intermediate level, the basis of probability theory and some of its more relevant theoretical features; (ii) to explore those aspects of the theory most used in ...
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... (1) A random variable X has E(X) = −4 and E(X 2 ) = 30. Let Y = −3X + 7. Compute: (a) V (X) = E(X 2 ) − E(X)2 = 14 (b) V (Y ) = (−3)2 V (X) = 126 (c) E((X + 5)2 ) = E(X 2 + 10X + 25) = E(X 2 ) + 10E(X) + 25 = 15 (d) E(Y 2 ) = V (Y ) + E(Y )2 = 126 + (−3E(X) + 7)2 = 487 (2) A deck has only face cards ...
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Syllabus - Boston University

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Venn Diagrams (7.2)

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Chapter 6 Section 3

< 1 ... 406 407 408 409 410 411 >

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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