Lecture 3
... generated by Xm , . . . , Xn , i.e., it is the σ-algebra generated by events of the form Xi−1 ((a, b]) for m ≤ i ≤ n and a < b. Definition 3.1 [Tail σ-algebra] The σ-algebra T := ∩n∈N Fn∞ is called the tail σ-algebra. Intuitively, T consists of events which do not depend on the values of any finite ...
... generated by Xm , . . . , Xn , i.e., it is the σ-algebra generated by events of the form Xi−1 ((a, b]) for m ≤ i ≤ n and a < b. Definition 3.1 [Tail σ-algebra] The σ-algebra T := ∩n∈N Fn∞ is called the tail σ-algebra. Intuitively, T consists of events which do not depend on the values of any finite ...
Real Numbers - Universidad de Buenos Aires
... If O is 0n and effectively hard for the class 0n ({0,1} ) we give a method to define sets that are 0n+m and 0n+m effectively hard, for every m. ...
... If O is 0n and effectively hard for the class 0n ({0,1} ) we give a method to define sets that are 0n+m and 0n+m effectively hard, for every m. ...
Lecture 10, January 28, 2004
... It is more likely to rain tomorrow if there is a solid cloud cover than if there are patches of blue. For the events “rain” and “blue patches”, the following value might apply: Pr[rain|blue patches] = 0.30 The event “rain” is listed first, and .30 is the conditional probability of that event; the co ...
... It is more likely to rain tomorrow if there is a solid cloud cover than if there are patches of blue. For the events “rain” and “blue patches”, the following value might apply: Pr[rain|blue patches] = 0.30 The event “rain” is listed first, and .30 is the conditional probability of that event; the co ...
No Slide Title
... "If a reference retrieval system’s response to each request is a ranking of the documents in the collections in order of decreasing probability of usefulness to the user who submitted the request, where the probabilities are estimated as accurately a possible on the basis of whatever data is made av ...
... "If a reference retrieval system’s response to each request is a ranking of the documents in the collections in order of decreasing probability of usefulness to the user who submitted the request, where the probabilities are estimated as accurately a possible on the basis of whatever data is made av ...
2.10. Strong law of large numbers If Xn are i.i.d with finite mean, then
... Let A = {ω : G ω has an infinite connected component}. If there is an infinite component, changing X e for finitely many e cannot destroy it. Conversely, if there was no infinite cluster to start with, changing X e for finitely many e cannot create one. In other words, A is a tail event for the coll ...
... Let A = {ω : G ω has an infinite connected component}. If there is an infinite component, changing X e for finitely many e cannot destroy it. Conversely, if there was no infinite cluster to start with, changing X e for finitely many e cannot create one. In other words, A is a tail event for the coll ...
PPT Chapter Six Discrete Probability Distributions
... 2000, 18.3% of all households have 3 or more cars. A researcher believes this percentage has increased since then. He conducts a simple random sample of 400 households and found that 82 households had 3 or more cars. Is this result unusual if the percentage of households with 3 or more cars is still ...
... 2000, 18.3% of all households have 3 or more cars. A researcher believes this percentage has increased since then. He conducts a simple random sample of 400 households and found that 82 households had 3 or more cars. Is this result unusual if the percentage of households with 3 or more cars is still ...
lab3
... Failure-time distributions have their own terminology. If f(x), F(x) denote the pdf and cdf of the time to failure, X, of some product, the probability P(X>t) is denoted by R(t) and is called the reliability of the product at time t. Viewed as a function, it is called the reliability function, or th ...
... Failure-time distributions have their own terminology. If f(x), F(x) denote the pdf and cdf of the time to failure, X, of some product, the probability P(X>t) is denoted by R(t) and is called the reliability of the product at time t. Viewed as a function, it is called the reliability function, or th ...
here for U8 text. - Iowa State University
... First, one may examine their joint probability. If Pr(A∩B)=Pr(A)Pr(B), then A and B are independent. Likewise, for bivariate random variables, if fX,Y(x,y)=fX(x)fY(y), then the X and Y are independent. Second, one may examine the conditional probabilities. If Pr(A|B)=Pr(A) or if Pr(B|A)=Pr(B), then ...
... First, one may examine their joint probability. If Pr(A∩B)=Pr(A)Pr(B), then A and B are independent. Likewise, for bivariate random variables, if fX,Y(x,y)=fX(x)fY(y), then the X and Y are independent. Second, one may examine the conditional probabilities. If Pr(A|B)=Pr(A) or if Pr(B|A)=Pr(B), then ...
Chap004
... calculate P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5). Or, one may use the BINOMDIST function to get the cumulative probability P(X 1), and then calculate the answer as its complement, namely, 1P(X 1). An easier way is to use the template shown in Figure 4.2.1. After making sure that n is filled ...
... calculate P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5). Or, one may use the BINOMDIST function to get the cumulative probability P(X 1), and then calculate the answer as its complement, namely, 1P(X 1). An easier way is to use the template shown in Figure 4.2.1. After making sure that n is filled ...
Lecture - Sybil Nelson
... a randomly chosen point on the surface. Let M = the maximum depth (in meters), so that any number in the interval [0, M] is a possible value of X. If we “discretize” X by measuring depth to the nearest meter, then possible values are nonnegative integers less than or equal to M. The resulting discre ...
... a randomly chosen point on the surface. Let M = the maximum depth (in meters), so that any number in the interval [0, M] is a possible value of X. If we “discretize” X by measuring depth to the nearest meter, then possible values are nonnegative integers less than or equal to M. The resulting discre ...
The Laws of Large Numbers Compared
... Many introductory probability texts treat this topic superficially, and more than once their vague formulations are misleading or plainly wrong. In this note, we consider a special case to clarify the relationship between the Weak and Strong Laws. The reason for doing so is that I have not been able ...
... Many introductory probability texts treat this topic superficially, and more than once their vague formulations are misleading or plainly wrong. In this note, we consider a special case to clarify the relationship between the Weak and Strong Laws. The reason for doing so is that I have not been able ...
File
... Suppose that 10% of the boxes of a certain cereal have a coupon for a free gallon of milk. If I were to buy only that brand of cereal, a. What is the probability that I won’t get a coupon until the 20th box? ...
... Suppose that 10% of the boxes of a certain cereal have a coupon for a free gallon of milk. If I were to buy only that brand of cereal, a. What is the probability that I won’t get a coupon until the 20th box? ...
File
... (a) What is the probability that the person is a man? We first compute the total number of people in the study. Total number of men = 14.0 + 29.6 + 15.6 + 7.2 + 17.5 + 10.1 = 94.0 Total number of women = 13.7 + 31.9 + 17.5 + 9.6 + 19.2 + 9.1 = 101.0 There are 94.0 million men and 101.0 million women ...
... (a) What is the probability that the person is a man? We first compute the total number of people in the study. Total number of men = 14.0 + 29.6 + 15.6 + 7.2 + 17.5 + 10.1 = 94.0 Total number of women = 13.7 + 31.9 + 17.5 + 9.6 + 19.2 + 9.1 = 101.0 There are 94.0 million men and 101.0 million women ...
3.2-contingeny-table-practice
... *Remember that P(B|A) means that event A occurred first, and that is the category you look at; it will be the denominator of your fraction. Then find the number of times event B occurred out of event A; that will be your numerator. I have done a few for you. The table below shows the gender of a sam ...
... *Remember that P(B|A) means that event A occurred first, and that is the category you look at; it will be the denominator of your fraction. Then find the number of times event B occurred out of event A; that will be your numerator. I have done a few for you. The table below shows the gender of a sam ...
Exp/Log Practice
... number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. Pythagorean Theorem Bill of Rights ...
... number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. Pythagorean Theorem Bill of Rights ...