Exercise 5. Here is a network of five roads joining cities A, B, C Each of...
Question 1 (20 points: Events, counting, and properties f probabniny Consider the network shown below. There are two kinds of links in the network. Each link of kind o-p +0 fails with probability p and that of kind O 4+0 fails with probability q. Each link is assumed to fail independently of the other. We say that a path is successful if no link in the path fails. For example, the path S-B-T succeeds if none of the links S...
C++ data structure problem. (Thanks) Traveling Salesman Problem Exercise Consider 5 cities of interest, namely a) Reno, b) San Francisco, c) Salt Lake City, d) Seattle, and e) Las Vegas. Use information on the road network and derive the miles from one city to the other. Then on that basis, conduct the following: Create a graph with each of its vertices correspond to one of these cities and its edges being weighted by the associated weights. Note that if...
(6) Each morning, twenty five police cadets are arranged like the entries of a 5 x 5 matrix. Each cadet forgets their cap with probability 1 -p, independently of the other cadets. Define random variables or more cadets in row i forgot their cap one 0:otherwise and or more cadets in column j forgot their cap : one Y,= 0 : otherwise X1 + X2++X +Yi+Y2++Y, Lastly, let Z (a) What is E(X,)? (b) What is P(X3 1 and Y21)?...
Multiple-choice questions each have five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to three such questions a. Use the multiplication rule to find P(WWC), where C denotes a correct answer and W denotes a wrong answer. P(WWC) (Type an exact answer.) b. Beginning with WWC, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the...
Multiple-choice questions each have five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find P(CCW), where C denotes a correct answer and W denotes a wrong answer. P(CCW)=(Type an exact answer.) b. Beginning with CCW, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list. P(CCW)- see...
Exercise 4-5 Algo A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.19, P(B) = 0.03, and P(C) 0.31 a. Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(D) 0.20 b. Find P(C). (Round your answer to 2 decimal places.) c. Find P(A U B). (Round your answer to 2 decimal places.) P(A U B) References eBook & Resources Worksheet Difficulty: 2 Medium Learning Objective: 04-03...
[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of all others. Let Y number of seedlings. 5. a) Find the pmf of Y b) Determine E(Y) and Var(Y).
5. Each of two schools A and B has a recruitment limit of 520 students: it ca number of candidates is equal to 1000, each candidate chooses, independently of the others, the school A or the school B (each choice has probability 1/2). nnot recruit more. The total (3 p.) Find the rough probability that all the students will be recruited to the universities they want. (7 p.) For which value of the recruitment limit, the probability that at least...
Problem 2 - Bayesian Inference Nisqually, Inc. sells books A,B,C on line. Each customer buys 0 or 1 copy of each title. a. Mrs. Independence Day, the company's data mining expert, makes the assumptions that: i) a customer decides to buy a book independently of what other books (s)he buys and independently of other customers. ii) all customers buy according to the same joint probability distribution PABC = PAPeP. with PA(1)0.6, PB(1) 0.3, Pc1) 0.4. For example, the probability that...
Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume that failures of different links are independent Link 1 Link 2 B A Link 5 Link 3 Link 4 1. Assume that p = 1/3. Find the probability that there exists a path from A to Balong which no link has failed. (Give a numerical answer.) 2. Given that exactly one link in the network has failed, find the probability...