PDF
... Let X = (X1 , . . . , Xn ) be a random vector with a given realization X(ω) = (x1 , . . . , xn ), where ω is the outcome (of an observation or an experiment) in the sample space Ω. A statistical model P based on X is a set of probability distribution functions of X: P = {FX }. If it is known in adva ...
... Let X = (X1 , . . . , Xn ) be a random vector with a given realization X(ω) = (x1 , . . . , xn ), where ω is the outcome (of an observation or an experiment) in the sample space Ω. A statistical model P based on X is a set of probability distribution functions of X: P = {FX }. If it is known in adva ...
Section 7-1 – How Probabilities are Determined
... perfect world we would expect to roll a 4 on a die 1 out of every 6 times so P(rolling a 4) = 1/6. Note that if we actually rolled a die several times we might NOT roll the number 4 one out of every 6 times. Maybe we rolled the 4 three out of 7 times. In that case the experimental probability would ...
... perfect world we would expect to roll a 4 on a die 1 out of every 6 times so P(rolling a 4) = 1/6. Note that if we actually rolled a die several times we might NOT roll the number 4 one out of every 6 times. Maybe we rolled the 4 three out of 7 times. In that case the experimental probability would ...
Math 1101 Counting Problems Handout #19
... 10. In how many ways can 8 dancers be arranged in a chorus line? 11. A bipartisan committee of ten people is being formed. The committee must be made up of six Democrats and four Republicans. If there are nine Democrats and six Republicans to choose from, in how many different ways can the Committee ...
... 10. In how many ways can 8 dancers be arranged in a chorus line? 11. A bipartisan committee of ten people is being formed. The committee must be made up of six Democrats and four Republicans. If there are nine Democrats and six Republicans to choose from, in how many different ways can the Committee ...
Document
... (The final quotient is the Bayes' theorem formula.) Note: Any problem that can be solved using Bayes' theorem can also be solved by setting up a two-way table. ...
... (The final quotient is the Bayes' theorem formula.) Note: Any problem that can be solved using Bayes' theorem can also be solved by setting up a two-way table. ...
Name: Signature: Math 5651 Lecture 003 (V. Reiner) Midterm Exam I
... Problem 2. (15 points) If I choose a rearrangement of the 9 letters in the word ”DISMISSED” into a possibly nonsensical string of 9 letters, with all rearrangements equally likely, then what is the probablity that at least one (and possibly more than one) of the following three events occurs?: • The ...
... Problem 2. (15 points) If I choose a rearrangement of the 9 letters in the word ”DISMISSED” into a possibly nonsensical string of 9 letters, with all rearrangements equally likely, then what is the probablity that at least one (and possibly more than one) of the following three events occurs?: • The ...
Continuous distributions In contrast to discrete random variables
... 1 standard deviation of the mean; about 95% of the time the value falls within two standard deviations of the mean. Example. Historical data suggest that the daily change in the Dow Jones Industrial Average is normally distributed, with standard deviation about 1.5% of the DJIA value. In a “flat” ma ...
... 1 standard deviation of the mean; about 95% of the time the value falls within two standard deviations of the mean. Example. Historical data suggest that the daily change in the Dow Jones Industrial Average is normally distributed, with standard deviation about 1.5% of the DJIA value. In a “flat” ma ...
Statistical Analysis of Gene Expression Data (A Large
... • Probability of an outcome in an experiment is the proportion of times that this particular outcome would occur in a very large (“infinite”) number of replicated experiments • Probability distribution describes the probability of any outcome in an experiment • If we have two different experiments, ...
... • Probability of an outcome in an experiment is the proportion of times that this particular outcome would occur in a very large (“infinite”) number of replicated experiments • Probability distribution describes the probability of any outcome in an experiment • If we have two different experiments, ...
FinalReview45 F12
... Ch. 1: Definitions, including types of data (True/False or Multiple Choice). Ch. 2: Definitions; frequency distributions, including class midpoint & relative frequency; histograms; stem & leaf plots; dot plot. Ch. 3: Definitions; mean, median, mode, midrange; range; standard deviation; mean and stan ...
... Ch. 1: Definitions, including types of data (True/False or Multiple Choice). Ch. 2: Definitions; frequency distributions, including class midpoint & relative frequency; histograms; stem & leaf plots; dot plot. Ch. 3: Definitions; mean, median, mode, midrange; range; standard deviation; mean and stan ...
here
... If Xi is his RBI count for each game, then Xi has mean .7, variance .04. If X is his number of RBIs for the season, then X has mean 162 × .7 = 113.4 and variance 162 × .04 = 6.48. By CLT, X ≈ N (113.4, 6.48). Since RBIs come in whole numbers only, we must use a continuity correction. The probability ...
... If Xi is his RBI count for each game, then Xi has mean .7, variance .04. If X is his number of RBIs for the season, then X has mean 162 × .7 = 113.4 and variance 162 × .04 = 6.48. By CLT, X ≈ N (113.4, 6.48). Since RBIs come in whole numbers only, we must use a continuity correction. The probability ...
Chapter 3
... Example: A fair coin is tossed 5 times, and a head (H) or a tail (T) is recorded each time. What is the probability of A = {exactly one head in 5 tosses}, and B = {exactly 5 heads}? The outcomes consist of a sequence of 5 H’s and T’s A typical outcome: HHTTH There are 32 possible outcomes, all equa ...
... Example: A fair coin is tossed 5 times, and a head (H) or a tail (T) is recorded each time. What is the probability of A = {exactly one head in 5 tosses}, and B = {exactly 5 heads}? The outcomes consist of a sequence of 5 H’s and T’s A typical outcome: HHTTH There are 32 possible outcomes, all equa ...
Solution
... 3. (a) What does it mean to say that E, F and G are independent events in a sample space S? Solution: The definition is that P(E ∩ F ) = P(E)P(F ), P(E ∩ G) = P(E)P(G), P(F ∩ G) = P(F )P(G) and P(E ∩ F ∩ G) = P(E)P(F )P(G). (b) Let E, F and G be three independent events in a sample space S. Prove th ...
... 3. (a) What does it mean to say that E, F and G are independent events in a sample space S? Solution: The definition is that P(E ∩ F ) = P(E)P(F ), P(E ∩ G) = P(E)P(G), P(F ∩ G) = P(F )P(G) and P(E ∩ F ∩ G) = P(E)P(F )P(G). (b) Let E, F and G be three independent events in a sample space S. Prove th ...
Random Codes - Haverford College
... messages that could get thru – redundancy. Excess redundancy gives us the room required to bring the error rate down. For a large n, pick M random codewords from {0, 1}n. ...
... messages that could get thru – redundancy. Excess redundancy gives us the room required to bring the error rate down. For a large n, pick M random codewords from {0, 1}n. ...
Name: Signature: Math 5651 Lecture 002 (V. Reiner) Midterm Exam I
... Problem 7. (15 points) Assume X = P oi(λ) is a Poisson random variable with mean λ, and let Y = X 2 , so that Y only takes on the values k 2 for k = 0, 1, 2, . . ., and λk Pr(Y = k 2 ) = e−λ . k! What is the expected value E(Y ) of Y ? (Hint: I think it helps to rewrite k 2 = k(k − 1) + k.) ...
... Problem 7. (15 points) Assume X = P oi(λ) is a Poisson random variable with mean λ, and let Y = X 2 , so that Y only takes on the values k 2 for k = 0, 1, 2, . . ., and λk Pr(Y = k 2 ) = e−λ . k! What is the expected value E(Y ) of Y ? (Hint: I think it helps to rewrite k 2 = k(k − 1) + k.) ...
PowerPoint プレゼンテーション
... and 4 from the computer science department, if there are 9 faculty members in the mathematics department and 11 of the computer science department? Solution By the product rule, the answer is the product of the number of 3 - combinatio ns of a set with 9 elements and the number of 4 - combinatio ns ...
... and 4 from the computer science department, if there are 9 faculty members in the mathematics department and 11 of the computer science department? Solution By the product rule, the answer is the product of the number of 3 - combinatio ns of a set with 9 elements and the number of 4 - combinatio ns ...
Ch4 HW Solution
... 1) What is a probability experiment? A probability experiment is a chance process that leads to well-defined outcomes. 2) Define sample space. The set of all possible outcomes of a probability experiment is called a sample space. 3) What is the difference between an outcome and an event? An outcome ...
... 1) What is a probability experiment? A probability experiment is a chance process that leads to well-defined outcomes. 2) Define sample space. The set of all possible outcomes of a probability experiment is called a sample space. 3) What is the difference between an outcome and an event? An outcome ...
