Handout 2
... a. goes 5 straight years with no accident (Answer=0.7738) b. has exactly 1 accident in 5 years (Answer=0.2036) c. has exactly 2 accidents in 5 years (Answer=0.0214) d. has at least 1 accident in 5 years (Answer=0.2262) e. has at most 4 accidents in 5 years (Answer=0.999999688) Counting rule: If a jo ...
... a. goes 5 straight years with no accident (Answer=0.7738) b. has exactly 1 accident in 5 years (Answer=0.2036) c. has exactly 2 accidents in 5 years (Answer=0.0214) d. has at least 1 accident in 5 years (Answer=0.2262) e. has at most 4 accidents in 5 years (Answer=0.999999688) Counting rule: If a jo ...
Notes 2
... not countable. For example, any open interval in the real line is not countable. Definition 4.3 (Outcomes and events). Let S be the sample space for a random experiment. An individual member of S is called an outcome of the experiment. Any collection of outcomes of S (i.e. a subset of S) is said to ...
... not countable. For example, any open interval in the real line is not countable. Definition 4.3 (Outcomes and events). Let S be the sample space for a random experiment. An individual member of S is called an outcome of the experiment. Any collection of outcomes of S (i.e. a subset of S) is said to ...
Topic 14 Notes Jeremy Orloff 14 Probability: Discrete Random Variables
... Example 14.5. Roll two dice. Let A = ’the total is < 4’. What is P (A)? answer: We know A = {2, 3}, that is, the ‘total is less than 4’ means that the total is either 2 or 3. Using the table for the probablities of the sum of two dice given in an earlier example we get P (A) = P (2 or 3) = P (2) + P ...
... Example 14.5. Roll two dice. Let A = ’the total is < 4’. What is P (A)? answer: We know A = {2, 3}, that is, the ‘total is less than 4’ means that the total is either 2 or 3. Using the table for the probablities of the sum of two dice given in an earlier example we get P (A) = P (2 or 3) = P (2) + P ...
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.