Numerical Integration (with a focus on Monte Carlo integration)
... Quadrature rule: an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. ...
... Quadrature rule: an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. ...
6.436J Lecture 17: Convergence of random
... gence in distribution is consistent with the definition of convergence of real numbers. This would not have been the case if the definition required the condition limn→∞ Fn (x) = F (x) to hold at every x. (c) Note that this definition just involves the marginal distributions of the ran dom variables i ...
... gence in distribution is consistent with the definition of convergence of real numbers. This would not have been the case if the definition required the condition limn→∞ Fn (x) = F (x) to hold at every x. (c) Note that this definition just involves the marginal distributions of the ran dom variables i ...
IN MEMORIAM Lester Eli Dubins
... While still in Chicago, Lester met Jimmie Savage (then on the mathematics faculty there) and surprised him by showing him that, contrary to accepted wisdom, the “bold strategy”— betting the largest amount consistent with the goal — is not uniquely optimal in the game of roulette if the goal is to ma ...
... While still in Chicago, Lester met Jimmie Savage (then on the mathematics faculty there) and surprised him by showing him that, contrary to accepted wisdom, the “bold strategy”— betting the largest amount consistent with the goal — is not uniquely optimal in the game of roulette if the goal is to ma ...
Lesson 1: The General Multiplication Rule
... Point out that the event of getting an airplane in the first box purchased and then getting an airplane in the second box purchased is an example of what are called independent events. Students worked with independent and dependent events in Algebra II. Review that two events are independent of each ...
... Point out that the event of getting an airplane in the first box purchased and then getting an airplane in the second box purchased is an example of what are called independent events. Students worked with independent and dependent events in Algebra II. Review that two events are independent of each ...
s 35(delete answer E), 49 (ace not a face card), 60 (fix answer A)
... 1.1 toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2. This means that occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin 10 time ...
... 1.1 toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2. This means that occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin 10 time ...
Lecture 8: Spectral Graph Theory III
... is “large” if and only if there does not exists a set with small conductance. This observation relates to the speed of convergence to π, the stationary distribution. By this we mean, if we are to start at any vertex in the graph and take a random walk, how long does it take for the probability distr ...
... is “large” if and only if there does not exists a set with small conductance. This observation relates to the speed of convergence to π, the stationary distribution. By this we mean, if we are to start at any vertex in the graph and take a random walk, how long does it take for the probability distr ...
