Introduction to Probability Theory
... Throughout this section, let S be a sample space (for some experiment), and P : P(S) −→ [0, 1] a probability measure. We will refer to properties 1 and 2 of Definition 1.2.3 as Property 1 and Property 2 respectively. 1. Union and Intersection (“OR” and “AND”) Let A and B be events (subsets of S). Th ...
... Throughout this section, let S be a sample space (for some experiment), and P : P(S) −→ [0, 1] a probability measure. We will refer to properties 1 and 2 of Definition 1.2.3 as Property 1 and Property 2 respectively. 1. Union and Intersection (“OR” and “AND”) Let A and B be events (subsets of S). Th ...
No Slide Title
... of a discrete probability distribution. Describe the characteristics and compute probabilities using the binomial probability distribution. Describe the characteristics and compute probabilities using the hypergeometric distribution. Describe the characteristics and compute the probabilities using t ...
... of a discrete probability distribution. Describe the characteristics and compute probabilities using the binomial probability distribution. Describe the characteristics and compute probabilities using the hypergeometric distribution. Describe the characteristics and compute the probabilities using t ...
Independent and Dependent Events
... committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? Write probability statement for a girl first, then boy ...
... committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? Write probability statement for a girl first, then boy ...
Document
... • To Kolmogorov, the axioms of probability are a given (like commandments) and are the starting point for the theory of probability. • Cardano – the Italian polymath – discovered the rules (axioms) of probability as a way to gamble without a sure loss. • Some psychologists, like Khaneman and Tversk ...
... • To Kolmogorov, the axioms of probability are a given (like commandments) and are the starting point for the theory of probability. • Cardano – the Italian polymath – discovered the rules (axioms) of probability as a way to gamble without a sure loss. • Some psychologists, like Khaneman and Tversk ...
Slide 1
... Theoretical and Experimental Probability Equally likely outcomes have the same chance of occurring. When you toss a fair coin, heads and tails are equally likely outcomes. Favorable outcomes are outcomes in a specified event. For equally likely outcomes, the theoretical probability of an event is t ...
... Theoretical and Experimental Probability Equally likely outcomes have the same chance of occurring. When you toss a fair coin, heads and tails are equally likely outcomes. Favorable outcomes are outcomes in a specified event. For equally likely outcomes, the theoretical probability of an event is t ...
Probability-and-Induction
... We did a fair amount of deductive logic so far. The Final contains language like “construct a natural deduction from the premises ________ to the conclusion ________.” ...
... We did a fair amount of deductive logic so far. The Final contains language like “construct a natural deduction from the premises ________ to the conclusion ________.” ...
Chapter 8 Discrete probability and the laws of chance
... Consider the following experiment: We flip a coin and observe any one of two possible results: “heads” (H) or “tails” (T). A fair coin is one for which these results are equally likely. Similarly, consider the experiment of rolling a dice: A six-sided dice can land on any of its six faces, so that a ...
... Consider the following experiment: We flip a coin and observe any one of two possible results: “heads” (H) or “tails” (T). A fair coin is one for which these results are equally likely. Similarly, consider the experiment of rolling a dice: A six-sided dice can land on any of its six faces, so that a ...
binomial_old
... capacity, so callers have difficulty placing their calls. It may be on interest to know the number of attempts necessary in order to gain a connection. Suppose that we let p = 0.05 be the probability of a connection during a busy time. We are interested in know the probability that 5 attempts are ne ...
... capacity, so callers have difficulty placing their calls. It may be on interest to know the number of attempts necessary in order to gain a connection. Suppose that we let p = 0.05 be the probability of a connection during a busy time. We are interested in know the probability that 5 attempts are ne ...
BASIC COUNTING
... among students on probation. That is, if we look only at students on probation, what proportion of them are freshmen. Since there are 1000 students on probation and 600 of them are freshmen, then the proportion of freshmen among students on probation is 0.60. We denote this quantity by P(FR|P) and c ...
... among students on probation. That is, if we look only at students on probation, what proportion of them are freshmen. Since there are 1000 students on probation and 600 of them are freshmen, then the proportion of freshmen among students on probation is 0.60. We denote this quantity by P(FR|P) and c ...
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.