Lecture 2
... from a lottery, empirical observation) or s/he came up with them on her/his own. • The ultimate aim is to present a succinct way to capture rational human behavior when faced with situations of uncertainty. • This theory will not be perfect – we will point out many shortcomings. However, it is the b ...
... from a lottery, empirical observation) or s/he came up with them on her/his own. • The ultimate aim is to present a succinct way to capture rational human behavior when faced with situations of uncertainty. • This theory will not be perfect – we will point out many shortcomings. However, it is the b ...
Determine whether the events are independent or dependent. Then
... Since the outcome of tossing the red die does not affect the outcome of rolling the blue die, these events are independent. ...
... Since the outcome of tossing the red die does not affect the outcome of rolling the blue die, these events are independent. ...
Lecture Note 7
... randomly select a person who is male, and “Female” the event that randomly select a person who is female. Probability of randomly select a person who is male ...
... randomly select a person who is male, and “Female” the event that randomly select a person who is female. Probability of randomly select a person who is male ...
Empirical Probability
... empirical probability that a person selected at random from the 2000 surveyed uses Mastercard. Round to the nearest thousandth when necessary. ...
... empirical probability that a person selected at random from the 2000 surveyed uses Mastercard. Round to the nearest thousandth when necessary. ...
Level 1 Mathematics, 2009 - SMC-Math
... 5% of Sarah’s DVDs that are less than two hours in length are scratched. Sarah owns 258 DVDs. How many of her DVDs that are less than 2 hours in length would you expect to be a comedy and scratched? Use probabilities and/or diagrams to explain and support your answer. ...
... 5% of Sarah’s DVDs that are less than two hours in length are scratched. Sarah owns 258 DVDs. How many of her DVDs that are less than 2 hours in length would you expect to be a comedy and scratched? Use probabilities and/or diagrams to explain and support your answer. ...
Probability - Mrs A`s Weebly
... Say whether each of these events is ‘certain’, ‘likely’, ‘unlikely’ or impossible to occur. a.) You will live in the same house for the rest of your life b.) You will toss a die and roll a ‘six’ c.) The sun will set in the west tonight d.) It will be colder where in February than in August e.) The ...
... Say whether each of these events is ‘certain’, ‘likely’, ‘unlikely’ or impossible to occur. a.) You will live in the same house for the rest of your life b.) You will toss a die and roll a ‘six’ c.) The sun will set in the west tonight d.) It will be colder where in February than in August e.) The ...
Tests of Significance
... 4) Name the procedure (One sample mean or prop. z test)/write the formula, find pvalue, reject or fail to reject Ho 5) Interpret your results in the context of the problem. (There is/is not sufficient evidence to suggest… ) The NULL HYPOTHESIS (H0 pronounced "H-nought") declares that there is NO eff ...
... 4) Name the procedure (One sample mean or prop. z test)/write the formula, find pvalue, reject or fail to reject Ho 5) Interpret your results in the context of the problem. (There is/is not sufficient evidence to suggest… ) The NULL HYPOTHESIS (H0 pronounced "H-nought") declares that there is NO eff ...
Fundamental Principles of Counting
... probability of 0.9 to the event, “the defendant is guilty”. You feel 90% sure that the defendant is guilty. Here, repetition of the event doesn’t make sense. However, the axioms of probability must still hold for this type of subjective probability assignment. The sample space is S = {guilty, innoce ...
... probability of 0.9 to the event, “the defendant is guilty”. You feel 90% sure that the defendant is guilty. Here, repetition of the event doesn’t make sense. However, the axioms of probability must still hold for this type of subjective probability assignment. The sample space is S = {guilty, innoce ...
probability-stats
... There are 3 red beads and 5 blue beads in a box. I pick a bead at random. The probability that it is red is 3/5. ...
... There are 3 red beads and 5 blue beads in a box. I pick a bead at random. The probability that it is red is 3/5. ...
2.4 Bernoulli Trials/Binomial Experiments
... What if we want to find the probability that he makes at most 7 free throws? We could add up P (X = 0) + P (X = 1) + · · · + P (X = 7), but there is another command on the calculator that will do this for us: binomcdf. This command is found on the same menu as binompdf and is option binomcdf. ...
... What if we want to find the probability that he makes at most 7 free throws? We could add up P (X = 0) + P (X = 1) + · · · + P (X = 7), but there is another command on the calculator that will do this for us: binomcdf. This command is found on the same menu as binompdf and is option binomcdf. ...
A Survey of Probability Concepts
... Sum of Classical Probabilities If a set of events is mutually exclusive and collectively exhaustive, then the sum of the probabilities is 1. Mutually exclusive: occurrence of one event means that none of the other events can occur at the same time. Collectively exhaustive: at least one of the e ...
... Sum of Classical Probabilities If a set of events is mutually exclusive and collectively exhaustive, then the sum of the probabilities is 1. Mutually exclusive: occurrence of one event means that none of the other events can occur at the same time. Collectively exhaustive: at least one of the e ...
Probability - East Penn School District
... What is the probability that you will select a yellow marble, not replace it, select a red marble, not replace it, and then select a yellow marble? ...
... What is the probability that you will select a yellow marble, not replace it, select a red marble, not replace it, and then select a yellow marble? ...
Paradoxes in Probability Theory
... theory is the study of internal properties of given probability models (or classes of probability models) satisfying Kolmogorov’s famous axioms from 1933 [Ko], the focus being on calculating or estimating probabilities or expectations of various events or quantities in such models. In contrast, issu ...
... theory is the study of internal properties of given probability models (or classes of probability models) satisfying Kolmogorov’s famous axioms from 1933 [Ko], the focus being on calculating or estimating probabilities or expectations of various events or quantities in such models. In contrast, issu ...
Probability Distributions
... A probability distribution is a function of the random variable X for all acceptable values of x. Probability distributions are often represented graphically, like the previous example. ...
... A probability distribution is a function of the random variable X for all acceptable values of x. Probability distributions are often represented graphically, like the previous example. ...
Probability/Data - Fall River Public Schools
... Step 3 When you follow the paths from left to right, you can find all the possible outcomes of tossing two coins. For example, the path shown in red represents the outcome heads-heads. ...
... Step 3 When you follow the paths from left to right, you can find all the possible outcomes of tossing two coins. For example, the path shown in red represents the outcome heads-heads. ...
No Slide Title
... Definition: tfij = fij / mi From DocumentFreq1.xls, there is one posting for monstrous in file19.txt From AllFiles1.xls, fij =1, mi = 16 tfij =1/16 = 0.0625 ...
... Definition: tfij = fij / mi From DocumentFreq1.xls, there is one posting for monstrous in file19.txt From AllFiles1.xls, fij =1, mi = 16 tfij =1/16 = 0.0625 ...
The Rate of Convergence of k, -NN Regression
... of misclassification conIEEE Trans. Inform. Theory, vol. IT-13, pp. 21-21, Jan. 1967. verges to the Bayes probability of error as rapidly as 0( n -‘/2fS), L. Gyorfi and Z. Gyorfi, “On the nonparametric estimate of a pos’teriori 6 > 0, where n is the length of the learning sequence. The rate is proba ...
... of misclassification conIEEE Trans. Inform. Theory, vol. IT-13, pp. 21-21, Jan. 1967. verges to the Bayes probability of error as rapidly as 0( n -‘/2fS), L. Gyorfi and Z. Gyorfi, “On the nonparametric estimate of a pos’teriori 6 > 0, where n is the length of the learning sequence. The rate is proba ...
A and B
... outcomes could happen, but we don’t know which particular outcome did or will happen. In general, each occasion upon which we observe a random phenomenon is called a trial. At each trial, we note the value of the random phenomenon, and call it an outcome. When we combine outcomes, the resulting comb ...
... outcomes could happen, but we don’t know which particular outcome did or will happen. In general, each occasion upon which we observe a random phenomenon is called a trial. At each trial, we note the value of the random phenomenon, and call it an outcome. When we combine outcomes, the resulting comb ...
Document
... Definition: tfij = fij / mi From DocumentFreq1.xls, there is one posting for monstrous ...
... Definition: tfij = fij / mi From DocumentFreq1.xls, there is one posting for monstrous ...
Dependent Events
... 2. Getting 3 red gumballs in a row out of a machine of different colors There is not enough information here to determine the probability but we know that the probability depends on how many red gumballs there are, and how many gumballs there are total. ...
... 2. Getting 3 red gumballs in a row out of a machine of different colors There is not enough information here to determine the probability but we know that the probability depends on how many red gumballs there are, and how many gumballs there are total. ...
13. A psychologist determined that the number of sessions required
... a. What is the probability that both cards dealt are aces or 10-point cards? b. What is the probability that both of the cards are aces? c. What is the probability that both of the cards have a point value of 10? d. A blackjack is a 10-point card and an ace for a value of 21. Use your answers to par ...
... a. What is the probability that both cards dealt are aces or 10-point cards? b. What is the probability that both of the cards are aces? c. What is the probability that both of the cards have a point value of 10? d. A blackjack is a 10-point card and an ace for a value of 21. Use your answers to par ...
PDF
... probability theory, evidence is associated with only one possible event. In DST, evidence can be associated with multiple possible events, i.e. sets of events. DST allows the direct representation of uncertainty. There are three important functions in DST by [3], [14]: (1) The basic probability assi ...
... probability theory, evidence is associated with only one possible event. In DST, evidence can be associated with multiple possible events, i.e. sets of events. DST allows the direct representation of uncertainty. There are three important functions in DST by [3], [14]: (1) The basic probability assi ...
Review: Independent and Dependent Events
... Solve these probability questions Example 1: Medical testing for a rare disease D = person has the disease, suppose: P(D) = 1/1000 = .001, P(DC) = .999 T = test for the disease is positive, suppose: P(T | D) = .95, so P(TC | D) = .05 P(T | DC) = .05, so P(TC | DC) = .95 So the test is 95% accurate ...
... Solve these probability questions Example 1: Medical testing for a rare disease D = person has the disease, suppose: P(D) = 1/1000 = .001, P(DC) = .999 T = test for the disease is positive, suppose: P(T | D) = .95, so P(TC | D) = .05 P(T | DC) = .05, so P(TC | DC) = .95 So the test is 95% accurate ...
Exam 1 Solution 1. (10 pts) The following circuit operates if and only
... speed}. Then P(I|L)=0.001, P(I|H)=0.01. P(H)=0.30 and P(L)=.70. We are looking for P(H|I). (a) First we compute the P(I) using the total probability rule: P(I)=P(I|H)P(H)+P(I|L)P(L)=(.01)(.30)+(.001)(.70)=.003+.0007=.0037. P(H|I)=P(I|H)P(H)]/P(I)=(.01)(.30)/.0037=3/3.7=.8108 4. (10 pts) An oil drill ...
... speed}. Then P(I|L)=0.001, P(I|H)=0.01. P(H)=0.30 and P(L)=.70. We are looking for P(H|I). (a) First we compute the P(I) using the total probability rule: P(I)=P(I|H)P(H)+P(I|L)P(L)=(.01)(.30)+(.001)(.70)=.003+.0007=.0037. P(H|I)=P(I|H)P(H)]/P(I)=(.01)(.30)/.0037=3/3.7=.8108 4. (10 pts) An oil drill ...
Dempster–Shafer theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty - a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence.In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints.