Chapter 5: Regression
... If two events A and B do not influence each other, and if knowledge about one does not change the probability of the other, the events are said to be independent of each other. Multiplication Rule for Independent Events Two events A and B are independent if knowing that one occurs does not change th ...
... If two events A and B do not influence each other, and if knowledge about one does not change the probability of the other, the events are said to be independent of each other. Multiplication Rule for Independent Events Two events A and B are independent if knowing that one occurs does not change th ...
Final - OSU Physics
... b) You are free to consult with any library book(s) you wish. If you do use references other than the notes and text please list them. c) Show your work. Do not just write down the answer (especially if you hope to get partial credit) ! PART 1 (280 points) 1) Short answer questions, each worth 5 poi ...
... b) You are free to consult with any library book(s) you wish. If you do use references other than the notes and text please list them. c) Show your work. Do not just write down the answer (especially if you hope to get partial credit) ! PART 1 (280 points) 1) Short answer questions, each worth 5 poi ...
Basics of Probability Theory and Bayesian Networks
... We adopt the following notations with respect to probability distributions and Boolean variables. Let X denote a variable; if X is a binary variable, e.g. taking either the value true or false, X = true is also denoted by simply x; similarly, X = false is also referred to by ¬x. Furthermore, when it ...
... We adopt the following notations with respect to probability distributions and Boolean variables. Let X denote a variable; if X is a binary variable, e.g. taking either the value true or false, X = true is also denoted by simply x; similarly, X = false is also referred to by ¬x. Furthermore, when it ...
TPS4e_Ch5_5.3
... has happened is denoted by P(B | A). Read | as “given that” or “under the condition that” ...
... has happened is denoted by P(B | A). Read | as “given that” or “under the condition that” ...
E(X 2 )
... squares of the distances from that is E((x - )2) As usual, this calculation can get hairy, but, as usual, there is a short cut, based on the formula: E((x - )2) = E(x2) - In words, you compute the expected value of the squares (no distances) and subtract the mean squared. Let's do an example ...
... squares of the distances from that is E((x - )2) As usual, this calculation can get hairy, but, as usual, there is a short cut, based on the formula: E((x - )2) = E(x2) - In words, you compute the expected value of the squares (no distances) and subtract the mean squared. Let's do an example ...
Interlude: Practice Midterm 1
... 2. Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together (i.e., every husband-wife pair occupies adjacent seats). (b) Compute the probability that at most one wife does not sit next to her husband. 3. Consider the following game. Th ...
... 2. Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together (i.e., every husband-wife pair occupies adjacent seats). (b) Compute the probability that at most one wife does not sit next to her husband. 3. Consider the following game. Th ...
Caffeine
... variables has a distribution that is normal with mean equal to the mean of any of them, and with a variance that is 1/n times the variance of any of them. [Note: since they all have the same (i.e. identical) distribution, then they all have the same mean and the same variance.] So, for such large va ...
... variables has a distribution that is normal with mean equal to the mean of any of them, and with a variance that is 1/n times the variance of any of them. [Note: since they all have the same (i.e. identical) distribution, then they all have the same mean and the same variance.] So, for such large va ...
Bayesian Networks and Hidden Markov Models
... Previous probabilities from our light readings: p(575|w1) = .05, p(575|w2) = .25 P(w1|575) = 0.05 X 0.8 / ((.05 X 0.8)+(0.25 X 0.2)) = .44 P(w2|575) = 0.25 X 0.2 / ((.05 X 0.8)+(0.25 X 0.2)) = .56 In this case, the additional evidence from the colorimeter leads us to guess that it is an ...
... Previous probabilities from our light readings: p(575|w1) = .05, p(575|w2) = .25 P(w1|575) = 0.05 X 0.8 / ((.05 X 0.8)+(0.25 X 0.2)) = .44 P(w2|575) = 0.25 X 0.2 / ((.05 X 0.8)+(0.25 X 0.2)) = .56 In this case, the additional evidence from the colorimeter leads us to guess that it is an ...
Ch. 4-6 PowerPoint Review
... The Variance, Var(X) = is the amount of variability from µ that we expect to see in X. The Standard Deviation of X, Var(X) for a Discrete X ...
... The Variance, Var(X) = is the amount of variability from µ that we expect to see in X. The Standard Deviation of X, Var(X) for a Discrete X ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.