1. A jar has 3 red balls, 2 white balls and 1 blue ball. A ball is
... “house”? (Hint, your results for 7 or 8 will be useful in this problem.) 10. A 25 question, multiple guess quiz is given to a class. Each question has 3 answers to select from. Let x be the number of questions answered correctly. Use the binomial distribution to find: a. P(x = 20) b. P(x < 20) c. P( ...
... “house”? (Hint, your results for 7 or 8 will be useful in this problem.) 10. A 25 question, multiple guess quiz is given to a class. Each question has 3 answers to select from. Let x be the number of questions answered correctly. Use the binomial distribution to find: a. P(x = 20) b. P(x < 20) c. P( ...
數學系計算機慨論期中考題
... (b) What is the probability that in exactly three of the next eight years no earthquakes will occur? (10%) Hint: in (b), you can suppose that a year is called a success if during its course no earthquakes occur. Ans: (a) Let N(t) be the number of earthquakes in this region at or prior to t, we are ...
... (b) What is the probability that in exactly three of the next eight years no earthquakes will occur? (10%) Hint: in (b), you can suppose that a year is called a success if during its course no earthquakes occur. Ans: (a) Let N(t) be the number of earthquakes in this region at or prior to t, we are ...
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 ...
Section 4.1
... a standard deck of cards. (1 out of 52 cards). Classical b. An economist predicts a 20% chance that technology stocks will decrease in value over the next year. Subjective c. A police officer wishes to know the probability that a driver, chosen at random, will be driving under the influence of alcoh ...
... a standard deck of cards. (1 out of 52 cards). Classical b. An economist predicts a 20% chance that technology stocks will decrease in value over the next year. Subjective c. A police officer wishes to know the probability that a driver, chosen at random, will be driving under the influence of alcoh ...
PPT
... Idea: turn events into numbers Let S be a sample space Defn: mapping from events to real numbers Example: X = the number on a die after a roll event “rolling a 1” -> 1 Technically, X is a function, ...
... Idea: turn events into numbers Let S be a sample space Defn: mapping from events to real numbers Example: X = the number on a die after a roll event “rolling a 1” -> 1 Technically, X is a function, ...
Faculty of Arts and Sciences - EMU
... Probability related matters and their practical use, Essential statistical knowledge towards statistical decision making. On successful completion of this course, all students will have developed their appreciation of and respect for values and attitudes regarding the issues of: Probability’s ...
... Probability related matters and their practical use, Essential statistical knowledge towards statistical decision making. On successful completion of this course, all students will have developed their appreciation of and respect for values and attitudes regarding the issues of: Probability’s ...
Lecture 5
... informs you that about 60% cases have success and you find this number too low and depressing. But if the Doctor looked at the proportion of success among young patients he would have observed that 85% of young patients have success (and that number is not so bad!). So often, while calculating proba ...
... informs you that about 60% cases have success and you find this number too low and depressing. But if the Doctor looked at the proportion of success among young patients he would have observed that 85% of young patients have success (and that number is not so bad!). So often, while calculating proba ...
STAT 724/ECO 761 Spring 2007 Problem Set Four Solutions
... We showed in class that this symmetric random walk will eventually return to 0 with probability 1. Compute the expected time it takes to return to 0, and show that it is infinity. I.e. the symmetric random walk, starting at 0, will return to 0 with probability 1, but it will take infinitely long to ...
... We showed in class that this symmetric random walk will eventually return to 0 with probability 1. Compute the expected time it takes to return to 0, and show that it is infinity. I.e. the symmetric random walk, starting at 0, will return to 0 with probability 1, but it will take infinitely long to ...
Tutorial Chapter 1
... accident the previous year. If a driver in that age bracket is randomly selected, what is the probability he/she will be involved in an accident? 10) A company produces 10 microchips during a nightshift. 6 of these turn out to be defective. Suppose 3 of the chips were sent to a customer. What is the ...
... accident the previous year. If a driver in that age bracket is randomly selected, what is the probability he/she will be involved in an accident? 10) A company produces 10 microchips during a nightshift. 6 of these turn out to be defective. Suppose 3 of the chips were sent to a customer. What is the ...
Probability Quiz
... A coin is biased in such a way that in the long run, on the average, a head turns up 3 times in 10 tosses. If this biased coin is tossed simultaneously with an unbiased coin, what is the probability that both will fall as heads? ...
... A coin is biased in such a way that in the long run, on the average, a head turns up 3 times in 10 tosses. If this biased coin is tossed simultaneously with an unbiased coin, what is the probability that both will fall as heads? ...
HW2_solutions
... (b) There are 10 points in S where y>x. P(y>x) = 10/25 = 2/5. (c) Find the probability that the first tag has a prime number and the second tag has an even number (1 is not considered a prime number) Solution: The points are : {22},{24},{32},{34},{52},{54}. P=6/25 = 0.24. There are 4 roads connectin ...
... (b) There are 10 points in S where y>x. P(y>x) = 10/25 = 2/5. (c) Find the probability that the first tag has a prime number and the second tag has an even number (1 is not considered a prime number) Solution: The points are : {22},{24},{32},{34},{52},{54}. P=6/25 = 0.24. There are 4 roads connectin ...
stdin (ditroff) - Purdue Engineering
... 3. (Spread-sheet question.) Consider a column of 100 spread-sheet cells each containing the code "=if (rand()< .6, 1, 0)". Suppose that Cell A1 contains the sum of the 100 cells. (a) What is the distribution name associated with Cell A1? -------------------------------------------------------------- ...
... 3. (Spread-sheet question.) Consider a column of 100 spread-sheet cells each containing the code "=if (rand()< .6, 1, 0)". Suppose that Cell A1 contains the sum of the 100 cells. (a) What is the distribution name associated with Cell A1? -------------------------------------------------------------- ...
Name Period Special Topics – Section 8.1 Probability Models and
... 2. This event is certain. It will occur on every trial of the random phenomenon. 3. This event is very unlikely, but it will occur once in a while in a long sequence of trials. 4. This event will occur more often than not. 2. Of voters in a recent election, 57% were male, 64% were Democrat, and 35% ...
... 2. This event is certain. It will occur on every trial of the random phenomenon. 3. This event is very unlikely, but it will occur once in a while in a long sequence of trials. 4. This event will occur more often than not. 2. Of voters in a recent election, 57% were male, 64% were Democrat, and 35% ...
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.