Lecture 2
... Roughly speaking, a consequentalist believes that the end result is what matters, not the path that got there. The validity/worthwhileness of a path is to be judged according to its outcome. This may seem amoral – but a consequentalist would say that if there are particular values attached to the pa ...
... Roughly speaking, a consequentalist believes that the end result is what matters, not the path that got there. The validity/worthwhileness of a path is to be judged according to its outcome. This may seem amoral – but a consequentalist would say that if there are particular values attached to the pa ...
Probability Review
... The binomial distribution tells us that the probability of getting m successes in n trials when the success probability is p is Cn,m pm (1 − p)n−m The first factor gives the number of ways to pick the m trials on which success happens. The second gives the probability of any particular outcome with ...
... The binomial distribution tells us that the probability of getting m successes in n trials when the success probability is p is Cn,m pm (1 − p)n−m The first factor gives the number of ways to pick the m trials on which success happens. The second gives the probability of any particular outcome with ...
Homework 3 - UCLA Statistics
... Use the binomialP theorem (go back to your classnotes from the beginning of the course) to show that if n X ∼ b(n, p) then x=0 p(x) = 1. EXERCISE 2 New York Lotto is played as follows: Out of 59 numbers 6 are chosen at random without replacement. Then from the remaining 53 numbers 1 is chosen. This ...
... Use the binomialP theorem (go back to your classnotes from the beginning of the course) to show that if n X ∼ b(n, p) then x=0 p(x) = 1. EXERCISE 2 New York Lotto is played as follows: Out of 59 numbers 6 are chosen at random without replacement. Then from the remaining 53 numbers 1 is chosen. This ...
Section 6.2 ~ Basics of Probability Objective: After this section you
... Section 6.2 ~ Basics of Probability Objective: After this section you will know how to find probabilities using theoretical and relative frequency methods and understand how to construct basic probability distributions. ...
... Section 6.2 ~ Basics of Probability Objective: After this section you will know how to find probabilities using theoretical and relative frequency methods and understand how to construct basic probability distributions. ...
AA2 Chapter 7 and 11 Quiz REVIEW
... 16. What is the probability of being dealt a 7-card hand that is all hearts? (HINT: first determine how many possible 7-card hands can be dealt from the hearts only; then determine how many total 7card hands can be dealt). ...
... 16. What is the probability of being dealt a 7-card hand that is all hearts? (HINT: first determine how many possible 7-card hands can be dealt from the hearts only; then determine how many total 7card hands can be dealt). ...
Ontario Mathematics Curriculum expectations
... A-2.5 determine, through investigation using class generated data and technology-based simulation models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator), the tendency of experimental probability to approach theoretical probability as the number of trials in an e ...
... A-2.5 determine, through investigation using class generated data and technology-based simulation models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator), the tendency of experimental probability to approach theoretical probability as the number of trials in an e ...
ECE 541 Probability Theory and Stochastic Processes Fall 2014
... 3. The conditional expectation as a projection; properties of conditional expectations; connection to optimal nonlinear estimation; some dynamical stochastic systems. 4. Random vectors and elements of parameter estimation. Joint distribution and densities with examples, Gaussian random vectors, char ...
... 3. The conditional expectation as a projection; properties of conditional expectations; connection to optimal nonlinear estimation; some dynamical stochastic systems. 4. Random vectors and elements of parameter estimation. Joint distribution and densities with examples, Gaussian random vectors, char ...
Introduction Introduction to probability theory
... To properly describe the probability distribution of X we need Pr(XB) for all BԹ. However, it suffices to know Pr(XB) for all B = (-,x] where xԹ. Definition. The distribution function, FX, of the random variable X is given by ...
... To properly describe the probability distribution of X we need Pr(XB) for all BԹ. However, it suffices to know Pr(XB) for all B = (-,x] where xԹ. Definition. The distribution function, FX, of the random variable X is given by ...
Conditional Probability Objectives: • Find the probability of an event
... A personal computer manufacturer buys 38% of its chips from Japan and the rest from America. 1.7% of the Japanese chips are defective, and 1.1% of the American chips are defective. • Find the probability that a chip is defective and made in Japan. • Find the probability that a chip is defective and ...
... A personal computer manufacturer buys 38% of its chips from Japan and the rest from America. 1.7% of the Japanese chips are defective, and 1.1% of the American chips are defective. • Find the probability that a chip is defective and made in Japan. • Find the probability that a chip is defective and ...
PowerPoint
... • When outcomes are equally likely, probabilities for events are easy to find just by counting. {Classical Method} • When the k possible outcomes are equally likely, each has a probability of 1/k. • For any event A that is made up of equally countof outcomes in A . likely outcomes, P A countof al ...
... • When outcomes are equally likely, probabilities for events are easy to find just by counting. {Classical Method} • When the k possible outcomes are equally likely, each has a probability of 1/k. • For any event A that is made up of equally countof outcomes in A . likely outcomes, P A countof al ...
Problem Sheet 6
... (d) [For further exploration! ] In lectures we considered a simple random walk, which at each step goes up with probability p and down with probability 1 − p. Suppose the walk starts from site 1. By taking limits in the gambler’s ruin model, we showed that the probability that the walk ever hits sit ...
... (d) [For further exploration! ] In lectures we considered a simple random walk, which at each step goes up with probability p and down with probability 1 − p. Suppose the walk starts from site 1. By taking limits in the gambler’s ruin model, we showed that the probability that the walk ever hits sit ...
7.SP.6_11_28_12_formatted
... marble back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these results, predict the number of red marbles in the bag. (Adapted from SREB publication Getting Students Ready for Algebra I: What Middle Grades Students Need to Know and Be Able to Do) ...
... marble back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these results, predict the number of red marbles in the bag. (Adapted from SREB publication Getting Students Ready for Algebra I: What Middle Grades Students Need to Know and Be Able to Do) ...
Oh Craps!
... Oh Craps! AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College ...
... Oh Craps! AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College ...
Chapter 4: Probability Rare Event Rule for Inferential Statistics Rare
... As a procedure is repeated many, many times, the relative frequency probability (from Rule 1) of an event tends to approach the actual probability (Rule 2 for equally likely outcomes) ...
... As a procedure is repeated many, many times, the relative frequency probability (from Rule 1) of an event tends to approach the actual probability (Rule 2 for equally likely outcomes) ...
Fibonacci*s Numbers
... A pointer is spun once on a circular spinner. The probability assigned to the pointer landing on a given integer is the ratio of the area of the corresponding circular sector to the area of the whole circle, as given in the table: ...
... A pointer is spun once on a circular spinner. The probability assigned to the pointer landing on a given integer is the ratio of the area of the corresponding circular sector to the area of the whole circle, as given in the table: ...
Conditional Probability
... homeowner’s policies, and 25% have both types of policies. If a customer is randomly selected, what is the probability that he or she has at least one of these two types of policies with the ...
... homeowner’s policies, and 25% have both types of policies. If a customer is randomly selected, what is the probability that he or she has at least one of these two types of policies with the ...
3.2 Conditional Probability and the Multiplication Rule
... surgery to Palos Community Hospital and General Hospital along with their survival status for the month of July. Palos ...
... surgery to Palos Community Hospital and General Hospital along with their survival status for the month of July. Palos ...
KOLMOGOROV ON THE ROLE OF RANDOMNESS IN
... applicability problem also drawn from the work of von Mises? My goal in this article is thus two-fold: (i) to answer Q1 by outlining the ways in which Kolmogorov drew upon von Mises’ work in addressing the applicability problem, and (ii) to answer Q2 by arguing that although Kolmogorov’s initial defi ...
... applicability problem also drawn from the work of von Mises? My goal in this article is thus two-fold: (i) to answer Q1 by outlining the ways in which Kolmogorov drew upon von Mises’ work in addressing the applicability problem, and (ii) to answer Q2 by arguing that although Kolmogorov’s initial defi ...
5.3 Conditional Probability, Dependent Events, Multiplication Rule
... replacement, it is reasonable to assume independence of the events. As a general rule, if the sample size is less than 5% of the population, then treat the events as independent. Find the probability that at least 1 male out of 1000, aged 24, will die during the course of the year if the probab ...
... replacement, it is reasonable to assume independence of the events. As a general rule, if the sample size is less than 5% of the population, then treat the events as independent. Find the probability that at least 1 male out of 1000, aged 24, will die during the course of the year if the probab ...
AP STATS – Chapter 8 Binomial vs. Geometric Probabilities Name 1
... 2. An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If the archer shoots 6 arrows, a) Define the variable X. b) Construct a pdf (probability distribution function) table for the variable X. ...
... 2. An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If the archer shoots 6 arrows, a) Define the variable X. b) Construct a pdf (probability distribution function) table for the variable X. ...
Example 3, Pg. 253, #7
... We always have 0 <=P(A)<=1. Probabilities are always between zero and one. The probability of the opposite event, not A, written A^c, is P(A^c)=1-P(A). The probability of “either A occurs OR B occurs, OR BOTH occur” is P( A _ or _ B ) P( A) P( B ) P( A _ AND _ B ) . The SUM RULE: A and B are M ...
... We always have 0 <=P(A)<=1. Probabilities are always between zero and one. The probability of the opposite event, not A, written A^c, is P(A^c)=1-P(A). The probability of “either A occurs OR B occurs, OR BOTH occur” is P( A _ or _ B ) P( A) P( B ) P( A _ AND _ B ) . The SUM RULE: A and B are M ...
Laws of Probability
... we are given that B has occurred. We can also think of B as the data gathered about the universe and A as the prediction based on this data. In that case P (A|B) can be seen as the probability of correct-ness of our prediction A given the data B already gathered. (Intelligence can be seen as the cap ...
... we are given that B has occurred. We can also think of B as the data gathered about the universe and A as the prediction based on this data. In that case P (A|B) can be seen as the probability of correct-ness of our prediction A given the data B already gathered. (Intelligence can be seen as the cap ...
(dominant) r: wrinkled seed (recessive)
... Up: If a mother rabbit is hybrid for black fur, and black fur is dominant, how would you write her alleles? ...
... Up: If a mother rabbit is hybrid for black fur, and black fur is dominant, how would you write her alleles? ...
12.4 Probability of Compound Events
... A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event. ◦ The card is not a king. ◦ The card is not an ace or a jack. ...
... A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event. ◦ The card is not a king. ◦ The card is not an ace or a jack. ...
History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics.The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods.