Exercise (change of variables)
... Exercise (joint probability of discrete r.v.’s) A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold on a given day, and let Y denote the numb ...
... Exercise (joint probability of discrete r.v.’s) A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold on a given day, and let Y denote the numb ...
Converses to the Strong Law of Large Numbers
... In the special case that the {Xn } are independent random variables, the tail events have a simple structure which is described by Kolmogorov’s Zero-One Law: In this case if E is a tail event, then P (E) is either zero or one. The proof consists of showing that every tail event E is independent of ...
... In the special case that the {Xn } are independent random variables, the tail events have a simple structure which is described by Kolmogorov’s Zero-One Law: In this case if E is a tail event, then P (E) is either zero or one. The proof consists of showing that every tail event E is independent of ...
Conditional probability and independence Bernoulli trials and the
... Independence of more than two events: Surprisingly, there are situations in which three or more events are independent of each other in pairs but are not independent of one another more generally. See the bottom of page 24 for an example. Events A1 , A2 , A3 , ... are independent if and only if the ...
... Independence of more than two events: Surprisingly, there are situations in which three or more events are independent of each other in pairs but are not independent of one another more generally. See the bottom of page 24 for an example. Events A1 , A2 , A3 , ... are independent if and only if the ...
D group task in discrete math: Edited at 10am 10 April 2017
... 15. How are the Multiplication, Addition, Pigeon-Hole, and Inclusion-Exclusion principles used in probability? 16. What are independent random variables and how the compound probability is given in this case? 17. What are dependent random variables and how the compound probability is given in this c ...
... 15. How are the Multiplication, Addition, Pigeon-Hole, and Inclusion-Exclusion principles used in probability? 16. What are independent random variables and how the compound probability is given in this case? 17. What are dependent random variables and how the compound probability is given in this c ...
Unit 10
... When making judgments about probability, what must be true about the probability if one were to support an alternative hypothesis? ...
... When making judgments about probability, what must be true about the probability if one were to support an alternative hypothesis? ...
Economics 302 Quiz #1
... A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require a slight adjustment. (12 points) a. What is the appropriate probability distribution for the number of defective frames in a random sample of 20 frames? D ...
... A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require a slight adjustment. (12 points) a. What is the appropriate probability distribution for the number of defective frames in a random sample of 20 frames? D ...
Probability Review hwk (5/22)
... 5. A card is drawn, a die is rolled and a coin is tossed. Find the probability of each outcome. a. The queen of hearts, a two and a tails, b. A face card, a number more than three, and a heads. 6. You are taking a true/false quiz with 9 questions. What is the probability of getting all 9 questions c ...
... 5. A card is drawn, a die is rolled and a coin is tossed. Find the probability of each outcome. a. The queen of hearts, a two and a tails, b. A face card, a number more than three, and a heads. 6. You are taking a true/false quiz with 9 questions. What is the probability of getting all 9 questions c ...
Binomial random variables
... 3. The probability is 0.04 that a person reached on a “cold call” by a telemarketer will make a purchase. If the telemarketer calls 40 people, what is the probability that at least one sale with ...
... 3. The probability is 0.04 that a person reached on a “cold call” by a telemarketer will make a purchase. If the telemarketer calls 40 people, what is the probability that at least one sale with ...
Stat 537: Introduction to Mathematical Statistics 1
... Conditional Probability Random Variables and their Distribution, Expectations, Moments Parametric Families of Distributions Limit Theorems Evaluation: Homework Midterm Exam Final Exam ...
... Conditional Probability Random Variables and their Distribution, Expectations, Moments Parametric Families of Distributions Limit Theorems Evaluation: Homework Midterm Exam Final Exam ...
Stats Review Lecture 5 - Limit Theorems 07.25.12
... • A sequence of random variables, X1, X2, …, converges in probability to a random variable X if, for every e > 0, ...
... • A sequence of random variables, X1, X2, …, converges in probability to a random variable X if, for every e > 0, ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.