Math 425 Introduction to Probability Lecture 5
... Nondiscrete sample space. Not all subsets of a nondiscrete sample space can be events (which have some probability of occurring). This issue will never be a problem for us in this class. It is actually hard to construct such events in the continuous sample spaces in which we will be most interested. ...
... Nondiscrete sample space. Not all subsets of a nondiscrete sample space can be events (which have some probability of occurring). This issue will never be a problem for us in this class. It is actually hard to construct such events in the continuous sample spaces in which we will be most interested. ...
Notes on Statistical Tests
... If D is 3, for example, then it follows from (2) that the probability of long newsworthy events approaches .001. We want to show: (3) P ROPOSITION : With probability 1, there are infinitely many newsworthy initial segments in S. We provide two proofs of the proposition. The first is swifter but the ...
... If D is 3, for example, then it follows from (2) that the probability of long newsworthy events approaches .001. We want to show: (3) P ROPOSITION : With probability 1, there are infinitely many newsworthy initial segments in S. We provide two proofs of the proposition. The first is swifter but the ...
The Addition Rules
... 1. In a box there are 3 red pens, 5 blue pens, and 2 black pens. If a person selects a pen at random, find the probability that the pen is: a.)A blue or a red pen, b.) A red or a black pen. 2. A small automobile dealer has 4 Buicks, 7 Fords, 3 Chryslers, and 6 Chevrolets. If a car is selected at ran ...
... 1. In a box there are 3 red pens, 5 blue pens, and 2 black pens. If a person selects a pen at random, find the probability that the pen is: a.)A blue or a red pen, b.) A red or a black pen. 2. A small automobile dealer has 4 Buicks, 7 Fords, 3 Chryslers, and 6 Chevrolets. If a car is selected at ran ...
The Addition Rules Mutually Exclusive Events Many problems in
... 1. In a box there are 3 red pens, 5 blue pens, and 2 black pens. If a person selects a pen at random, find the probability that the pen is: a.)A blue or a red pen, b.) A red or a black pen. 2. A small automobile dealer has 4 Buicks, 7 Fords, 3 Chryslers, and 6 Chevrolets. If a car is selected at r ...
... 1. In a box there are 3 red pens, 5 blue pens, and 2 black pens. If a person selects a pen at random, find the probability that the pen is: a.)A blue or a red pen, b.) A red or a black pen. 2. A small automobile dealer has 4 Buicks, 7 Fords, 3 Chryslers, and 6 Chevrolets. If a car is selected at r ...
Conditional Probability
... The same result holds if B = “The first die is k” and 2 ≤ k ≤ 6. Carrying this reasoning further, we see that given the outcome lies in A, all five possibilities have the same probability. This should not be surprising. The original probability is uniform over the 36 possibilities, so when we condit ...
... The same result holds if B = “The first die is k” and 2 ≤ k ≤ 6. Carrying this reasoning further, we see that given the outcome lies in A, all five possibilities have the same probability. This should not be surprising. The original probability is uniform over the 36 possibilities, so when we condit ...
Lesson 6 Part 2 Probability Distributions for Discrete Random
... ‘Success’ is defined as survival for at least 5 years n = number of ‘trials’ = 10 subjects π = probability of success = 0.80, assumed to be constant for all subjects X is the number of patients surviving at least 5 years. X can range from 0 - 10 ...
... ‘Success’ is defined as survival for at least 5 years n = number of ‘trials’ = 10 subjects π = probability of success = 0.80, assumed to be constant for all subjects X is the number of patients surviving at least 5 years. X can range from 0 - 10 ...
Experiments
... increased or decreased by other events. The probability that there is no final for this class is very low. But IF I die, the probability is much higher. And IF Lingnan closes, the probability is much much higher. We say that the probability of P IF Q is the probability of P conditional on Q. ...
... increased or decreased by other events. The probability that there is no final for this class is very low. But IF I die, the probability is much higher. And IF Lingnan closes, the probability is much much higher. We say that the probability of P IF Q is the probability of P conditional on Q. ...
Lecture 3
... Example 3.22: Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each locations L1, L2 , L3 and L4 are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0 ...
... Example 3.22: Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each locations L1, L2 , L3 and L4 are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0 ...
Lecture 16: Uncertainty 1 Victor R. Lesser
... Ubiquity of Uncertainty Most real domains are inaccessible, dynamic, and non-deterministic (at least from the agent’s perspective). In these domains, it is impossible for an agent to know the exact state of its environment. ...
... Ubiquity of Uncertainty Most real domains are inaccessible, dynamic, and non-deterministic (at least from the agent’s perspective). In these domains, it is impossible for an agent to know the exact state of its environment. ...
Students` Biases in Conditional Probability Reasoning
... Even when students progress towards the upper level in this classification, difficulties remain at high school and university (Tarr & Lannin, 2005). Below, we summarize various studies: Confusing causal and diagnostic situations: From a psychological point of view, the person who assesses a conditio ...
... Even when students progress towards the upper level in this classification, difficulties remain at high school and university (Tarr & Lannin, 2005). Below, we summarize various studies: Confusing causal and diagnostic situations: From a psychological point of view, the person who assesses a conditio ...
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.