Chapter 2: Probability
... Combinations (Order is not Important) Suppose that when we pick 3 letters out of the 6 letters A, B, C, D, E, and F we chose BCD, or BDC, or CBD, or CDB, or DBC, or DCB. (These are the 6 (3!) permutations or orderings of the 3 letters B, C, and D.) But these are orderings of the same combination of ...
... Combinations (Order is not Important) Suppose that when we pick 3 letters out of the 6 letters A, B, C, D, E, and F we chose BCD, or BDC, or CBD, or CDB, or DBC, or DCB. (These are the 6 (3!) permutations or orderings of the 3 letters B, C, and D.) But these are orderings of the same combination of ...
slides12 - Duke University
... Probability: Axiomatic Definition • Let p be any total function p:S→[0,1] such that ...
... Probability: Axiomatic Definition • Let p be any total function p:S→[0,1] such that ...
Chapter 6
... probability that out of six gears selected at random none will be defective? Exactly one? Exactly two? Exactly three? Exactly four? Exactly five? Exactly six out of six? ...
... probability that out of six gears selected at random none will be defective? Exactly one? Exactly two? Exactly three? Exactly four? Exactly five? Exactly six out of six? ...
Probability Models in Computer Science
... outcomes and a probability for each outcome. The sample space S of a chance process is the set of all possible outcomes. An event is an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space. A probability model is a description of some chance process ...
... outcomes and a probability for each outcome. The sample space S of a chance process is the set of all possible outcomes. An event is an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space. A probability model is a description of some chance process ...
Geometry Mathematics Curriculum Guide – Unit 8 Probability
... Understand independence and conditional probability and use them to interpret data S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S.CP ...
... Understand independence and conditional probability and use them to interpret data S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S.CP ...
Some discrete distributions
... Let X be an integer in the range 10..20. P(x) = 1/11 for x = 10,11,12,13,14,..20 To find E(X): Let Y be a number in the range 1..11. Thus, E(X) = (1+11)/2 = 6. Now, X = Y + 9. E(X) = E(Y+9) = E(Y) + 9 = 6+9 = 15 Var(X) = Var(Y+9) = Var(Y) = (112 – 1)/12 = 10 Note: the Discrete Uniform Distribution i ...
... Let X be an integer in the range 10..20. P(x) = 1/11 for x = 10,11,12,13,14,..20 To find E(X): Let Y be a number in the range 1..11. Thus, E(X) = (1+11)/2 = 6. Now, X = Y + 9. E(X) = E(Y+9) = E(Y) + 9 = 6+9 = 15 Var(X) = Var(Y+9) = Var(Y) = (112 – 1)/12 = 10 Note: the Discrete Uniform Distribution i ...
7 - DanShuster.com!
... 4. We are working with a geometric random variable with p=.8. (a) What is the probability that the first yes comes from the 3rd woman you ask? P(X=3) = (.2)2(.8)1 = geometpdf(.8,3) = .032 (b) What is the probability that it takes fewer than 3 women to get a yes answer? Fewer than 3, means less than ...
... 4. We are working with a geometric random variable with p=.8. (a) What is the probability that the first yes comes from the 3rd woman you ask? P(X=3) = (.2)2(.8)1 = geometpdf(.8,3) = .032 (b) What is the probability that it takes fewer than 3 women to get a yes answer? Fewer than 3, means less than ...
7.1: Discrete and Continuous Random Variables
... 4. We are working with a geometric random variable with p=.8. (a) What is the probability that the first yes comes from the 3rd woman you ask? P(X=3) = (.2)2(.8)1 = geometpdf(.8,3) = .032 (b) What is the probability that it takes fewer than 3 women to get a yes answer? Fewer than 3, means less than ...
... 4. We are working with a geometric random variable with p=.8. (a) What is the probability that the first yes comes from the 3rd woman you ask? P(X=3) = (.2)2(.8)1 = geometpdf(.8,3) = .032 (b) What is the probability that it takes fewer than 3 women to get a yes answer? Fewer than 3, means less than ...
Probability Fancy a Flutter
... By the End of Year 7 • Create a model of all possible outcomes and identify, e.g. that horse 7 can move as a result of 6 of the 36 possible outcomes. • Predict that this outcome should occur about once every 6 rolls of the dice, but recognise that the actual experimental results are unlikely to be ...
... By the End of Year 7 • Create a model of all possible outcomes and identify, e.g. that horse 7 can move as a result of 6 of the 36 possible outcomes. • Predict that this outcome should occur about once every 6 rolls of the dice, but recognise that the actual experimental results are unlikely to be ...
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.