Problem #4: A maintenance firm has gathered the following information regarding the failure mechanism for air conditioningsystems.Problem #4(a):Problem #4(b):Evidence ofYeselectrical failure NoProblem #4(c):Gas LeaksYes49If this is a representative sample of AC failure, find the following probabilities.(a) That there was evidence of electrical failure, given that there was a gas leak.(b) That there was a gas leak, given that there was evidence of electrical failure.(c) Let E be the event that there is a gas leak and let F be the event that there is evidence of electrical failure. FindPE F).20No1220Enter your answer symbolically,as in these examplesEnter your answer symbolically,as in these examplesEnter your answer symbolically,as in these examples

Given data is Gas Leaks Evidence of electrical failure Yes No Total Yes 49 12 61…

Answered: Problem #4: A maintenance firm has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Problem 2: You are developing a new gas exchange nozzle for scuba tanks that will be used in deep sea diving. The nozzles are rated to withstand pressures up to 12 atmospheres which is experienced at a depth of 120.7 meters. Up to this point, 96% of your nozzles in previous tests have functioned flawlessly at that depth. In testing your current iteration, 6 of the 200 nozzles tested failed at that depth. Can you claim a statistically significant improvement over previous tests with a significance level of 0.05? Why or why not? Use critical rejection criteria, P-values, or confidence intervals. Document your full process.
Problem 1 ( We consider an investment problem with 3 risky assets. You are given that The expected return rate of these three risky assets are ₁ = 0.08, 2₂ = 0.13 and T3 = 0.16 repsectively. The variances of return rate of three risky assets are o2 = 0.02, 0² = 0.05 and 03 = 0.1 respectively. ● ● ● We assume that the returns of the risky assets are mutually uncorrelated (i.e. cov(ri,ri) = 0 for all i ‡ j. (a) Find the minimum variance portfolio with expected return Up = 0.1 using Lagrange method. Is the portfolio efficient? Explain your answer. (*Note: You also need to demonstrate how do you solve the relevant equations in your solution.) (b) (True/False) Suppose that the investor is seeking for a portfolio which can achieve (1) smallest variance of portfolio return and (2) achieve expected return not less than μp (i.e. Tp Hp), then the investor conjectures that the optimal portfolio must be the minimum variance portfolio with expected return μp. Give your comment on the correctness of…
Problem#3 Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that ơ1 = 02 = 1.0 psi. From a random sample of size n1=30 and n2=35, you obtain x1=162.5 and x2=155.0. The company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi. a) Based on the sample information, should it use plastic 1? Use a = 0.05 in reaching a decision. b) Calculate a 95% confidence interval on the difference in means. What is your conclusion on the hypothesis based on this CI?
Questions 2-4 are based on the following scenario. Mr. Lange draws two independent random samples from normally-distributed popula- tions with unknown population means and unknown population vari- ances. The first sample is found to have x = 78, s² = 25, and n = = 10; while the second sample is found to have y = 74, s² : 9, and n = 16. 2. Mr. Lange wishes to know if there is enough evidence to conclude that the population variances differ. Answer the following questions. (a) State the competing theories of this test. (b) Are the requirements for the Equal Variances F Test met? If not, explain why. (c) Compute the F statistic. Round your answer to three decimal places. (d) What distribution does the F statistic have? (e) Compute ao as discussed in class. What conclusion can you draw?
Problem #2: Suppose a random variable X has expected value E[X] = 1 and variance Var(X) = 1. Compute the following quantities. Problem #2 (a): Problem #2(b): Problem #2(c): Problem #2 (d): Problem #2 Your Answer: 2(a) 2(b) 2(c) 2(d) (a) E[2X + 3] (b) E[X²] Your Mark: 2(a) 2(b) 2(c) 2(d) (c) E[(2X +3)²] (d) Var[2X +3] Attempt #1 Just Save Submit Problem #2 for Grading Attempt #2 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #3 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #4 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #5 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #6 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #7 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt #8 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d) Attempt # 9 2(a) 2(b) 2(c) 2(d) 2(a) 2(b) 2(c) 2(d)
Questions 2-4 are based on the following scenario. Mr. Lange draws two independent random samples from normally-distributed popula- tions with unknown population means and unknown population vari- ances. The first sample is found to have x = 78, s21 = 25, and n = 10; while the second sample is found to have y = 74, s2 = 9, and n = 16. 2. Mr. Lange wishes to know if there is enough evidence to conclude that the population variances differ. Answer the following questions. (a) State the competing theories of this test. (b) Are the requirements for the Equal Variances F Test met? If not, explain why. (c) Compute the F statistic. Round your answer to three decimal places. (d) What distribution does the F statistic have? (e) Compute α0 as discussed in class. What conclusion can you draw? 3. Mr. Lange wishes to use Welch’s T Test to determine whether there is enough evidence to conclude the population means differ. Answer the following questions. (a) State the…
Example 2: A meteorologist was interested in determining whether or not there was higher average rainfall during certain seasons of the year in her local community. She randomly sampled 7 days from each season and recorded the amount of rainfall in her local community on that day. Carry out an appropriate hypothesis test at the a = 0.02 level to determine if there is evidence that the true average rainfall is higher in some seasons than others. The data is shown below where the rainfall is measured in inches. %3D
Question 2 National Electronics Company buys parts from two subsidiaries. The quality control department at this company wanted to check if the distribution of good and defective parts is the same for the supplies of parts received from both subsidiaries. The quality control inspector selected a sample of 300 parts received frum Subsidiary A, sample of 400 parts received from Subsidiary B, and a sample of 450 parts received from Subsidiary C. These parts were checked for being good or defective. The following table records the results of this investigation. Subsidiary A 284 Subsidiary B 381 Subsidiary C 418 Good Defective 16 19 32 Using a 5% significance level, test the null hypothesis that the distributions of good and defective parts are the same for the three subsidiaries.

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