Lecture02
... functions. The first concerns the `non-decreasing' clause in the definition. `Nondecreasing' does not mean `increasing.' A `non-decreasing' function may coast along at a fixed y-value for a while. Step functions whose successive steps have increasing y coordinates are examples of functions that are ...
... functions. The first concerns the `non-decreasing' clause in the definition. `Nondecreasing' does not mean `increasing.' A `non-decreasing' function may coast along at a fixed y-value for a while. Step functions whose successive steps have increasing y coordinates are examples of functions that are ...
Lecture 1
... expectation of f (X) given Y , denoted by E[f (X)|Y ], is a function of the random variable Y , which is again a random variable. If Y in the above example is real-valued with a continuous distribution, i.e., P(Y = y) = 0 for all y ∈ R, then how can we define the conditional probability of X given Y ...
... expectation of f (X) given Y , denoted by E[f (X)|Y ], is a function of the random variable Y , which is again a random variable. If Y in the above example is real-valued with a continuous distribution, i.e., P(Y = y) = 0 for all y ∈ R, then how can we define the conditional probability of X given Y ...
Chapters 5-7 - ShareStudies.com
... Let A be the event that a new Wing Foot store makes over $540,000 its first year. Let B be the event that a store makes more than $540,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. The accounting offi ...
... Let A be the event that a new Wing Foot store makes over $540,000 its first year. Let B be the event that a store makes more than $540,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. The accounting offi ...
INDEPENDENT EVENTS and the MULTIPLICATION RULE
... Last Name____________________ First Name _______________________Class Time________Chapter 3-6 EXAMPLE 11: Statistics from the FHDA (Foothill/De Anza) district website for a recent quarter: 15% of students registered at De Anza College were Hispanic 15 % of students registered at Foothill Colleg ...
... Last Name____________________ First Name _______________________Class Time________Chapter 3-6 EXAMPLE 11: Statistics from the FHDA (Foothill/De Anza) district website for a recent quarter: 15% of students registered at De Anza College were Hispanic 15 % of students registered at Foothill Colleg ...
ML_Lecture_6
... Example:Assume that data points have been uniformly generated from k distinct Gaussian with the same known variance. The problem is to output a hypothesis h=<1, 2 ,.., k> that describes the means of each of the k distributions. In particular, we are looking for a maximum likelihood hypothesis f ...
... Example:Assume that data points have been uniformly generated from k distinct Gaussian with the same known variance. The problem is to output a hypothesis h=<1, 2 ,.., k> that describes the means of each of the k distributions. In particular, we are looking for a maximum likelihood hypothesis f ...
ML_Lecture_6
... Example:Assume that data points have been uniformly generated from k distinct Gaussian with the same known variance. The problem is to output a hypothesis h=<1, 2 ,.., k> that describes the means of each of the k distributions. In particular, we are looking for a maximum likelihood hypothesis f ...
... Example:Assume that data points have been uniformly generated from k distinct Gaussian with the same known variance. The problem is to output a hypothesis h=<1, 2 ,.., k> that describes the means of each of the k distributions. In particular, we are looking for a maximum likelihood hypothesis f ...
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.