Grade/Course: Geometry (Second Semester) Instructional Unit 10
... categories are associated with each with each object being classified. Use object being classified. the two-way table as a sample space -Use a two-way frequency table to to decide if events are independent decide if events are independent and and to approximate conditional to approximate conditional ...
... categories are associated with each with each object being classified. Use object being classified. the two-way table as a sample space -Use a two-way frequency table to to decide if events are independent decide if events are independent and and to approximate conditional to approximate conditional ...
Answers
... This is equivalent to 3p − 2p2 > 1, so −2p2 + 3p − 1 > 0. But −2p2 + 3p − 1 = 2(1 − p)(p − 1/2) > 0 only if p > 1/2 as 1 − p is always greater than 0. Hence a three-person jury is preferable if p > 1/2. If p < 1/2, the decision of a single juror is preferable. For p = 1/2 there is no difference. 9. ...
... This is equivalent to 3p − 2p2 > 1, so −2p2 + 3p − 1 > 0. But −2p2 + 3p − 1 = 2(1 − p)(p − 1/2) > 0 only if p > 1/2 as 1 − p is always greater than 0. Hence a three-person jury is preferable if p > 1/2. If p < 1/2, the decision of a single juror is preferable. For p = 1/2 there is no difference. 9. ...
Section 5.3 Conditional Probability and the
... has happened is denoted by P(B | A). Read | as “given that” or “under the condition that” ...
... has happened is denoted by P(B | A). Read | as “given that” or “under the condition that” ...
Name: Date: ______ Period: ______ Unit 2: Probability Unit
... 12. A deck contains 10 cards numbered 1 to 10. Suppose that Curtis chooses a card at random and then chooses a second card at random after replacing the first card. What is the probability that both cards are printed with an even number? ...
... 12. A deck contains 10 cards numbered 1 to 10. Suppose that Curtis chooses a card at random and then chooses a second card at random after replacing the first card. What is the probability that both cards are printed with an even number? ...
Probability and Randomness What is randomness? A phenomenon
... The weatherman notes that for the past several winters temperatures have been mild and there hasn’t been much snow. He obeserves, “Even though we’re not supposed to use the law of averages, we are due for a cold snowy winter this year!” A gambler knows red and black are equally-likely, but he has ju ...
... The weatherman notes that for the past several winters temperatures have been mild and there hasn’t been much snow. He obeserves, “Even though we’re not supposed to use the law of averages, we are due for a cold snowy winter this year!” A gambler knows red and black are equally-likely, but he has ju ...
GWAS
... (P-values) • P-value = probability of the observed data (or worse) under the null hypothesis • Example: – Suppose we are given a series of co in-tosses – We feel that a biased coin produced the tosses – We can ask the following question: what is the probability that a fair coin produced the tosses? ...
... (P-values) • P-value = probability of the observed data (or worse) under the null hypothesis • Example: – Suppose we are given a series of co in-tosses – We feel that a biased coin produced the tosses – We can ask the following question: what is the probability that a fair coin produced the tosses? ...
Probability - NC State Department of Statistics
... •Formal study of uncertainty •The engine that drives Statistics • Primary objective of lecture unit 4: 1. use the rules of probability to calculate appropriate measures of uncertainty. 2. Learn the probability basics so that we can do Statistical Inference ...
... •Formal study of uncertainty •The engine that drives Statistics • Primary objective of lecture unit 4: 1. use the rules of probability to calculate appropriate measures of uncertainty. 2. Learn the probability basics so that we can do Statistical Inference ...
Finding the Probability of an Event a.
... Two events A and B (from the same sample space) are mutually exclusive when A and B have no outcomes in common. In the terminology of sets, the intersection of A and B is the empty set, which implies that P(A B) = 0. ...
... Two events A and B (from the same sample space) are mutually exclusive when A and B have no outcomes in common. In the terminology of sets, the intersection of A and B is the empty set, which implies that P(A B) = 0. ...
6.1 The Idea of Probability
... Two ways to determine # of outcomes • Tree diagram • Multiplication principal – If we can do one task in ‘a’ number of ways and another task in ‘b’ number of ways, then both are done in ‘a x b’ number of ways. ...
... Two ways to determine # of outcomes • Tree diagram • Multiplication principal – If we can do one task in ‘a’ number of ways and another task in ‘b’ number of ways, then both are done in ‘a x b’ number of ways. ...
P(A B)
... • State the addition rule for disjoint events • State the general addition rule for union of two events • Given any two events A and B, compute P(A B) • Given two events, compute their joint probability • Use the general multiplication rule to define P(B | A) ...
... • State the addition rule for disjoint events • State the general addition rule for union of two events • Given any two events A and B, compute P(A B) • Given two events, compute their joint probability • Use the general multiplication rule to define P(B | A) ...
2.2 Let E and F be two events for which one knows that the
... R1 , what is the probability region R2 is infested as well? 3.10 A student takes a multiple-choice exam. Suppose for each question he either knows the answer or gambles and chooses an option at random. Further suppose that if he knows the answer, the probability of a correct answer is 1, and if he g ...
... R1 , what is the probability region R2 is infested as well? 3.10 A student takes a multiple-choice exam. Suppose for each question he either knows the answer or gambles and chooses an option at random. Further suppose that if he knows the answer, the probability of a correct answer is 1, and if he g ...
Lecture 1. Probabilities - Definitions, Examples and Basic Tools
... about outcome of an experiment, that express the chances that the statement is true. Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of ...
... about outcome of an experiment, that express the chances that the statement is true. Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of ...
Worksheet 4
... subject guesses correctly or not. If the subject merely guesses, the probability of success remains the same from trial to trial. Whether a subject guesses correctly or not on a trial is independent from the results of previous trials. b. Yes, X is a binomial random variable with n = 10 and p = .25. ...
... subject guesses correctly or not. If the subject merely guesses, the probability of success remains the same from trial to trial. Whether a subject guesses correctly or not on a trial is independent from the results of previous trials. b. Yes, X is a binomial random variable with n = 10 and p = .25. ...
recitation1
... A random variable is a function that associates a unique numerical value (a token) with every outcome of an experiment. (The value of the r.v. will vary from trial to trial as the experiment is repeated) ...
... A random variable is a function that associates a unique numerical value (a token) with every outcome of an experiment. (The value of the r.v. will vary from trial to trial as the experiment is repeated) ...
slides
... A random variable is a function that associates a unique numerical value (a token) with every outcome of an experiment. (The value of the r.v. will vary from trial to trial as the experiment is repeated) ...
... A random variable is a function that associates a unique numerical value (a token) with every outcome of an experiment. (The value of the r.v. will vary from trial to trial as the experiment is repeated) ...
File
... • Jared lost the dice to his favorite board game, but he does have a graphing calculator. According to the rules, the player should throw 2 dice and move the total number of spaces shown on the top of the 2 dice. • 1. What range of numbers does a single dice generate? What should he enter in his cal ...
... • Jared lost the dice to his favorite board game, but he does have a graphing calculator. According to the rules, the player should throw 2 dice and move the total number of spaces shown on the top of the 2 dice. • 1. What range of numbers does a single dice generate? What should he enter in his cal ...
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.