(1997). Sharpness of second moment criteria for branching and tree
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
Year-8-Curriculum-Overview-Autumn-Half-Term-2
... outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one ...
... outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one ...
Statistics
... Theorem 9: For any events A1 , . . . , An ∈ A we have P(A1 ∩ · · · ∩ An ) = P(A1 )P(A2 |A1 ) . . . P(An |A1 . . . An−1 ) provided P(A1 . . . An−1 ) > 0. Example 19: A fruit basket contains 25 apples and oranges of which 20 are apples. If three fruits are randomly picked in a sequence, what is the pr ...
... Theorem 9: For any events A1 , . . . , An ∈ A we have P(A1 ∩ · · · ∩ An ) = P(A1 )P(A2 |A1 ) . . . P(An |A1 . . . An−1 ) provided P(A1 . . . An−1 ) > 0. Example 19: A fruit basket contains 25 apples and oranges of which 20 are apples. If three fruits are randomly picked in a sequence, what is the pr ...
Learning Objectives Definition Experiment, Outcome, Event
... • There is a diagnostic technique to detect the disease, but it is not very accurate. Let B denote the event “test shows the disease is present.” Assume that historical evidence shows that if a person actually has the disease, the probability that the test will indicate the presence of the disease i ...
... • There is a diagnostic technique to detect the disease, but it is not very accurate. Let B denote the event “test shows the disease is present.” Assume that historical evidence shows that if a person actually has the disease, the probability that the test will indicate the presence of the disease i ...
Lec2
... • What is he most probable classification of the new instance given the training data? • The most probable classification of the new instance is obtained by combining the prediction of all hypothesis, weighted by their posterior probabilities ...
... • What is he most probable classification of the new instance given the training data? • The most probable classification of the new instance is obtained by combining the prediction of all hypothesis, weighted by their posterior probabilities ...
How to use the p value in decision making
... whether a phenomenon needs more attention. With a Bayesian justi cation for the use the p-value. Positive reactions and stimulating discussions encouraged me to investigate the consequences of my setup further. With a result that still amazes me. Apart from special cases, my conclusion can be summar ...
... whether a phenomenon needs more attention. With a Bayesian justi cation for the use the p-value. Positive reactions and stimulating discussions encouraged me to investigate the consequences of my setup further. With a result that still amazes me. Apart from special cases, my conclusion can be summar ...
Comm on Probability - rivier.instructure.com.
... most of these examples, too, it is not just one factor that determines probability, but multiple factors. For heart disease, family history, lifestyle, eating habits, work environment; you have to consider each factor as an individual probability & then combine these probabilities together to come u ...
... most of these examples, too, it is not just one factor that determines probability, but multiple factors. For heart disease, family history, lifestyle, eating habits, work environment; you have to consider each factor as an individual probability & then combine these probabilities together to come u ...
point estimate - Ursinus College Student, Faculty and Staff Web Pages
... mean of the population, we seek to give an interval estimate; that is, an interval in which we think the population mean lies (obviously the smaller the better). We will also be able to give a level of confidence which answers the question ‘how sure are you?’ e.g. 95% sure, 98% sure etc. Let’s show ...
... mean of the population, we seek to give an interval estimate; that is, an interval in which we think the population mean lies (obviously the smaller the better). We will also be able to give a level of confidence which answers the question ‘how sure are you?’ e.g. 95% sure, 98% sure etc. Let’s show ...
A and B
... Roughly speaking, this means that the outcome of one trial doesn’t influence or change the outcome of another. ...
... Roughly speaking, this means that the outcome of one trial doesn’t influence or change the outcome of another. ...
Review: Independent and Dependent Events
... Solve these probability questions Example 1: Medical testing for a rare disease D = person has the disease, suppose: P(D) = 1/1000 = .001, P(DC) = .999 T = test for the disease is positive, suppose: P(T | D) = .95, so P(TC | D) = .05 P(T | DC) = .05, so P(TC | DC) = .95 So the test is 95% accurate ...
... Solve these probability questions Example 1: Medical testing for a rare disease D = person has the disease, suppose: P(D) = 1/1000 = .001, P(DC) = .999 T = test for the disease is positive, suppose: P(T | D) = .95, so P(TC | D) = .05 P(T | DC) = .05, so P(TC | DC) = .95 So the test is 95% accurate ...
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.