Suppose that we have a sample space with five equally likely experimental outcomes: E₁, E₂, E3, E4, E5. Let1'A = {E₁, E3}B = {E₂, E4}C = {E₂, E3, E5}.(a) Find P(A), P(B), and P(C).P(A)P(B)P(C) ===(b) Find P(A U B).P(A U B) =Are A and B mutually exclusive?They ---Select--- ✓ mutually exclusive. (c) Find AC. (Enter your answer in set notation.)ACFind CC. (Enter your answer in set notation.)CC =Find P(AC) and P(CC).P(AC):P(CC):=(d) Find A U BC. (Enter your answer in set notation.)AU BC =Find P(A U BC).P(A U BC) ==(e) Find P(BU C).P(BU C) =

There are five equally likely outcomes which are as follows:To Find:a) b) Are they mutually…

Answered: Suppose that we have a sample space…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Suppose we have a sample space S {E, , E2 , E3 , E4, } Where E1 ,E2 , E3, E4 denote the sample points (outcomes) Where; P (E,) = 0.05, P(E2) = 0.20, P(E3)= 0.20, P(E4) = 0.25, %3D P(E,N E4) = 0.12 a) Find P(E, U E4) b) Find P(E,) c) Are (E2) and (E4) independent events d) Are (E, ) or (E4) mutually exclusive event?
Q. 14: The number of faculty and the number of students are shown for a random selection of small colleges in table. Is there a relationship between the two variables? Faculty Students 99 110 113 116 138 174 220 1353 1290 1091 1213 1384 1283 2075 Q. 15: Use the data Q14 Switch x and y and repeat the process. Which do you think is really the independent variable? Q. 16: Using the data Q14 find the coefficient of regression and comment on its sign. Q. 17: Fit the regression line on the data given in Q14. Q. 18: Plot data Ql14 on scatter plot and fit regression line on it and discuss errors.
A local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Assuming the conditions for inference have been met, what is the 90% confidence interval for the difference in proportions of households that would support starting the school year a week earlier?
Q.6 A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than 15 are heated by oil if, in a random sample of 1000 homes in this city, it is found that 136 are heated by oil?
Example 1 of the Chapter 9 Examples, we couldn't prove the player made over 80% of all of her free throws at the 1% significance level even though she made 53 out of 60 (which is 88.3%). (a) If she made 88.3% of the 60 free throws, why are we not able to show that she makes over 80%? (b) How many of the 60 would she have to make so that we could prove that she makes over 80% at the 1% significance level. Derive your answer mathematically (not by trial and error) (c) At what significance level would 53 out of 60 allowed us to prove she can make over 80%?
A researcher is investigating the effects of three different fertilizers (A, B, and C) on the growth of tomato plants. The height of the plants (in inches) is measured after one month using a sample of four plants for each fertilizer: Fertilizer A: [12, 14, 15, 13] Fertilizer B: [16, 17, 15, 18] Fertilizer C: [10, 11, 12, 9] Perform a one-way ANOVA to determine if there is a significant difference in the mean height of the tomato plants among the three fertilizers at a 5% significance level. Show all steps
You have been assigned to test the hypothesis that the average number of cars waiting in line for the drive-thru window during lunch hour differs between Chick-fil-A, Wendy's, and McDonald's. The following data show the number of cars in line during randomly selected times during the lunch hour at all three chains. Chick-fil-A(1) Wendy's(2) McDonald's(3) 7 7 6 10 8 7 11 5 6 8 3 7 9 2 9 Perform a one-way ANOVA using α = 0.05 to determine if a difference exists in the average number of cars waiting in line at the drive-thru during the lunch hour between these chains.
. In a study to investigate the effect of regular physical exercise on the reduction of high blood pressure in males aged 60-65, the researchers selected at random a sample of n₁ =12 males suffering from high blood pressure in the given a 12ge group and for a two-year period placed the subjects on a daily physical exercise program. A second sample of n₂ =12 males suffering from high blood pressure in the given age group was selected and again for the two-year period this group of subjects were placed on a physical exercise program for which they were required to perform only once a week. Finally a third sample of n3 =12 males suffering from high blood pressure in the given age group was selected. No exercise program was required for individuals in sample three. At the end of the two-year period the reduction in blood pressure was measured for each of the subjects in the study and is presented in the table on the next page. Table V.1: Reduction in Blood pressure for three groups of…
A researcher is interested in examining the effects of relaxation techniques on test performance. The researcher randomly selects thirty college students and randomly assigns them into two groups of fifteen each. One group receives training in several relaxation techniques and the second group receives no training. Each group is given a statistics test. The average score for the group that received the relaxation training was 75 (s² = 5) and the average for students who did not receive the relaxation training was 50 (s² = 8). (1) State the null and alternative hypotheses for this study (2) What is the dependent and independent variable for this study (3) What test statistic/hypothesis test would you select to determine if the means are significantly difference at the alpha .05 level? (4) What critical value would you use to make your decision to reject or retain the null hypothesis at alpha .05?
Need someone to double check my work.
b. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.
Given n independent policyholders with individual loss random variables X1, X2, ., Xn, such that the expected value of any policyholder's loss is pph and the variance is o. If the insurer is providing these n policyholders with insurance, find the following (the detailed steps are required): 1. The expected value of the insurer's average loss per policy; 2. The variance of the average loss per policy.

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