Lecture5_SP17_probability_history_solutions
... • “stochastic” from “stochos”: target, aim, guess • Early Christians: every event, no matter how trivial, was perceived to be a direct manifestation of God’s intervention • St. Augustine (354-430): “We say that those causes that are said to be by chance are not nonexistent but are hidden, and we att ...
... • “stochastic” from “stochos”: target, aim, guess • Early Christians: every event, no matter how trivial, was perceived to be a direct manifestation of God’s intervention • St. Augustine (354-430): “We say that those causes that are said to be by chance are not nonexistent but are hidden, and we att ...
No Slide Title
... • Problem. Buses arrive at a specified stop at 7:15am and 7:30am. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that she waits less than 5 minutes for the bus. Solution. We use a uniform r. v. on (0, 30). The desired probability i ...
... • Problem. Buses arrive at a specified stop at 7:15am and 7:30am. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that she waits less than 5 minutes for the bus. Solution. We use a uniform r. v. on (0, 30). The desired probability i ...
REMARKS ON FOUNDATIONS OF PROBABILITY
... 1. Formulas, Boolean algebras and models We shall here be interested in those formal theories in which only relational constants occur. Variables of higher orders (e.g. running over sets or classes of sets) may be allowed, but in such cases we shall assume that in the formulas each such variable is ...
... 1. Formulas, Boolean algebras and models We shall here be interested in those formal theories in which only relational constants occur. Variables of higher orders (e.g. running over sets or classes of sets) may be allowed, but in such cases we shall assume that in the formulas each such variable is ...
Applications of Number Theory in Computer Science Curriculum
... The program simulates the experiment many times; the results for all trials are added and then averaged at the end to obtain a final answer By simple laws of probability of sum of independent events , we know that the average value, produced by our program, will converge to the correct result ...
... The program simulates the experiment many times; the results for all trials are added and then averaged at the end to obtain a final answer By simple laws of probability of sum of independent events , we know that the average value, produced by our program, will converge to the correct result ...
Task - Illustrative Mathematics
... After students have had a chance to estimate the probability in part (c), you could follow up by asking them if they think that this number is exactly equal to the theoretical probability of getting 4, 5 or 6 heads when a coin is tossed. Then you can point out that this estimated probability is base ...
... After students have had a chance to estimate the probability in part (c), you could follow up by asking them if they think that this number is exactly equal to the theoretical probability of getting 4, 5 or 6 heads when a coin is tossed. Then you can point out that this estimated probability is base ...
Fundamental Principles of Counting
... the event doesn’t make sense. However, the axioms of probability must still hold for this type of subjective probability assignment. The sample space is S = {guilty, innocent}. It follows that P({innocent}) = 1 – P({guilty}) = 0.1. • Using the methods of Chapter 3, Conditional Probability and Indepe ...
... the event doesn’t make sense. However, the axioms of probability must still hold for this type of subjective probability assignment. The sample space is S = {guilty, innocent}. It follows that P({innocent}) = 1 – P({guilty}) = 0.1. • Using the methods of Chapter 3, Conditional Probability and Indepe ...
Targil 10
... It is not possible that neither of this two events take place: it'd mean we have both a column of zeroes, and a row of ones, and then in the intersection of these two would be a contradiction. This gives a non-strict inequality. It is easy to find a table where both events take place simultaneously; ...
... It is not possible that neither of this two events take place: it'd mean we have both a column of zeroes, and a row of ones, and then in the intersection of these two would be a contradiction. This gives a non-strict inequality. It is easy to find a table where both events take place simultaneously; ...
Probability box
),steps=500.png?width=300)
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.