Chapter 3: Conditional Probability and Independence
... P(AB), the probability that neither machine breaks down today? If we assume independence, P(AB) = P(A)P(B)—a straightforward calculation. If we do not assume independence, however, we cannot calculate P(AB) unless we form a model for their dependence structure or collect data on their joint performa ...
... P(AB), the probability that neither machine breaks down today? If we assume independence, P(AB) = P(A)P(B)—a straightforward calculation. If we do not assume independence, however, we cannot calculate P(AB) unless we form a model for their dependence structure or collect data on their joint performa ...
Lecture 10 Slides
... about the random variable in order to estimating the whole distribution All we are interested is the lower tail ...
... about the random variable in order to estimating the whole distribution All we are interested is the lower tail ...
Math 1312 - Business Math II
... Review of Sets: 1. The set that contains all elements under consideration is called the ________________________ set. 2. The sets A and B are said to be ________________________ provided A ∩ B = 3. If x A and x B, then x _________ and x ___________ ( either A or B) ( both A and B ) 4. The ...
... Review of Sets: 1. The set that contains all elements under consideration is called the ________________________ set. 2. The sets A and B are said to be ________________________ provided A ∩ B = 3. If x A and x B, then x _________ and x ___________ ( either A or B) ( both A and B ) 4. The ...
Day 1 - MSTE
... If they were mated there would be 2 pair of white socks, 3 pair of tan socks, and 5 pair of black socks. Draw a tree diagram that shows all of the possible ways of picking two socks from the drawer in the dark one sock at a time, without replacement. Then determine the probability that you pick a pa ...
... If they were mated there would be 2 pair of white socks, 3 pair of tan socks, and 5 pair of black socks. Draw a tree diagram that shows all of the possible ways of picking two socks from the drawer in the dark one sock at a time, without replacement. Then determine the probability that you pick a pa ...
Real Limits, Apparent Limits, and Frequency Distributions
... Although probability is a common term in the natural language, meaning likelihood or chance of occurrence, statisticians define it much more precisely. The probability of an event is the theoretical relative frequency of the event in a model of the population. The models that have been discussed up ...
... Although probability is a common term in the natural language, meaning likelihood or chance of occurrence, statisticians define it much more precisely. The probability of an event is the theoretical relative frequency of the event in a model of the population. The models that have been discussed up ...
8.2
... The student will be able to determine the union and intersection of events. The student will be able to determine the complement of an event. The student will be able to determine the odds of an event. The student will be able to solve applications of empirical probability. ...
... The student will be able to determine the union and intersection of events. The student will be able to determine the complement of an event. The student will be able to determine the odds of an event. The student will be able to solve applications of empirical probability. ...
Chapter 5
... We learned that one of the conditions required to apply the binomial distribution is that the trials are independent so the probability of the two outcomes remain constant. ...
... We learned that one of the conditions required to apply the binomial distribution is that the trials are independent so the probability of the two outcomes remain constant. ...
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.