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What Is Fuzzy Probability Theory?
What Is Fuzzy Probability Theory?

... incomplete knowledge of the system but the random variables (measurements) still have precise values. For example, when we flip a coin we have only a partial knowledge about the physical structure of the coin and the initial conditions of the flip. If our knowledge about the coin were complete, we c ...
Discrete Structures I - Faculty Personal Homepage
Discrete Structures I - Faculty Personal Homepage

... 6. What is the probability that a poker hand contains a full house, that is, three of one kind and two of another kind? 7. What is the probability that the numbers 11,4, 17, 39, and 23 are drawn in that order from a bin containing 50 balls labeled with the numbers 1, 2, . . . , 50 if a) the ball sel ...
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... • Uncountable standard Borel ⇒ Borel equivalent to ([0, 1], B) • Hence, by “subspace” (Ω, A) we need only consider 1 Ω ⊂ [0, 1] is finite, and A = P(Ω) ⊂ B (= the power set = collection of all subsets) 2 Ω ⊂ [0, 1] is countable, and again A = P(Ω) ⊂ B ...
Note 16: Random Variables: Distribution and Expectation
Note 16: Random Variables: Distribution and Expectation

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lecture13-probability

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... 28. The scores on the Harrison High School AP Stat Test #1 (T1) had a mean of 27 with a standard deviation of 3 and the scores on Test #2 (T2) had a mean of 29 with a standard deviation of 4. To reflect the true brilliance of the students taking the course, the total score had to be adjusted accord ...
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ORF 245 Fundamentals of Statistics Chapter 8 Hypothesis Testing

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... 2. Comment on the following statement: “Arithmetic mean is always the best measure of central tendency”. 3. Give the various measures of dispersion. 4. What is the probability of getting the sum as 5 when two dice are thrown? 5. The distribution function of a random variable ‘X’ is as follows: X: ...
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... letter once per word? The words don’t have to mean anything. Similarly (Exeter 89:9) how many nine-letter words can be formed from the letters of hyperbola? An extremely useful notation when dealing with permutations is n!, read “n factorial”. The definition is n! = n · (n − 1) · (n − 2) · · · 2 · 1 ...
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Topic 7: Probability

... Dr House is trying to find the cause of a disease. He suspects Lupus (as he always does) due to their kidney failure. The probability that someone has this symptom if they did have Lupus is 0.2. The probability that a random patient has kidney damage is 0.001, and the probability they have Lupus 0.0 ...
Quantifying Uncertainty
Quantifying Uncertainty

Topic 7: Probability
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... Dr House is trying to find the cause of a disease. He suspects Lupus (as he always does) due to their kidney failure. The probability that someone has this symptom if they did have Lupus is 0.2. The probability that a random patient has kidney damage is 0.001, and the probability they have Lupus 0.0 ...
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... With this approximation, we are now ready to answer the question: if we randomly survey 1000 Texas residents voted in 2012, how many of them had voted for President Obama? As analyzed earlier, we have X ∼ Binomial(n = 1000, p = 0.414). As n is large and p is close to neither 0 nor 1, we can approxim ...
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... OBJ: 12-6.1 Use measures of central tendency to represent a set of data. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5 TOP: Use measures of central tendency to represent a set of data. KEY: Measures of Central Tendency | Data | Represent Data 21. ANS: B If two events, A and B, are mutually exclusive, whic ...
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p.p chapter 6.3

... equal chance to be chosen. Patti is one of the students in this class. Let X= the number of Patti’s correct guesses 1) Show that X is a binomial random variable. 2) Find P(X=3), explain what this result means. 3) To get a passing score on the quiz, a student must guess correctly at least 6 times. Wo ...
Mathematics
Mathematics

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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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