5.1
... We’ll label the students in the AP Statistics class from 01 to 28, and the remaining students from 29 to 95. (Numbers from 96 to 00 will be skipped.) Starting at the randomly selected row 139 and moving left to right across the row, we’ll look at pairs of digits until we come across two different va ...
... We’ll label the students in the AP Statistics class from 01 to 28, and the remaining students from 29 to 95. (Numbers from 96 to 00 will be skipped.) Starting at the randomly selected row 139 and moving left to right across the row, we’ll look at pairs of digits until we come across two different va ...
CSC384: Intro to Artificial Intelligence Reasoning under Uncertainty
... this tell us anything more about how likely it is that the element also has property B? ■ If B is independent of A then we have learned nothing new about the likelihood of the element being a member of B. ...
... this tell us anything more about how likely it is that the element also has property B? ■ If B is independent of A then we have learned nothing new about the likelihood of the element being a member of B. ...
Mathematics for Business Decisions, Part II
... $18,000. (i) Use NORMDIST and Graphing.xlsm to plot the p.d.f., f X (x) . (ii) Use NORMDIST and Graphing.xlsm to plot the c.d.f., FX (x) . Solution. 11.. Let X be an exponential random variable with parameter 5 . (i) Use Graphing.xlsm to plot the p.d.f., f X , over the interval [0, 40] . (ii) Us ...
... $18,000. (i) Use NORMDIST and Graphing.xlsm to plot the p.d.f., f X (x) . (ii) Use NORMDIST and Graphing.xlsm to plot the c.d.f., FX (x) . Solution. 11.. Let X be an exponential random variable with parameter 5 . (i) Use Graphing.xlsm to plot the p.d.f., f X , over the interval [0, 40] . (ii) Us ...
Compound Probability March 10, 2014
... 2. Your drawer contains 6 red socks and 11 blue socks. It's too dark to see which are which, but you grab two anyway. What is the probability that both socks are red? ...
... 2. Your drawer contains 6 red socks and 11 blue socks. It's too dark to see which are which, but you grab two anyway. What is the probability that both socks are red? ...
conditional entropy
... A means of representing statistical phenomena inherent in a sample of data, namely p( y | x) A means of requiring that our model of the process exhibit these ...
... A means of representing statistical phenomena inherent in a sample of data, namely p( y | x) A means of requiring that our model of the process exhibit these ...
Lecture 20 and 21 1 PCP theorems using Parallel Repetition 2 H
... 1. Let φ be an instance of a 2CSP problem. It is said to have the projection property if for each constraint φr (y1 , y2 ) and each value of y1 there is an unique value of y2 such that φr (y1 , y2 ) = 1. In other words, knowing the value of y1 is enough to know the value of y2 such that φr (y1 , y2 ...
... 1. Let φ be an instance of a 2CSP problem. It is said to have the projection property if for each constraint φr (y1 , y2 ) and each value of y1 there is an unique value of y2 such that φr (y1 , y2 ) = 1. In other words, knowing the value of y1 is enough to know the value of y2 such that φr (y1 , y2 ...
Markov and Chebyshev`s Inequalities
... Question: A biased coin is flipped 200 times consecutively, and comes up heads with probability 1/10 each time it is flipped. Give an upper bound the probability that it will come up heads at least 120 times. Solution: Let X be the r.v. that counts the number of heads. Recall: E(X ) = 200 ∗ (1/10) = ...
... Question: A biased coin is flipped 200 times consecutively, and comes up heads with probability 1/10 each time it is flipped. Give an upper bound the probability that it will come up heads at least 120 times. Solution: Let X be the r.v. that counts the number of heads. Recall: E(X ) = 200 ∗ (1/10) = ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.