A certain market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X2 is as given in the accompanying table. X2 0 1 2 3 0 0.08 0.07 0.04 0.00 1 0.05 0.15 0.04 0.04 X1 2 0.05 0.04 0.10 0.06 3 0.00 0.04 0.04 0.07 4 0.00 0.02 0.05 0.06 (a) What is P(X₁ = 1, x2 = 1), that is, the probability that there is exactly one customer in each line? P(X₁ =1, X21) = (b) What is P(X₁ = X2), that is, the probability that the numbers of customers in the two lines are identical? P(X₁ = X2)= | (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. OA = {X₁ ≥ 2+ X₂ U X₂ ≤ 2 + X₁} = + 1 2 OA = {x₁ ≥2+ X₂ UX₂ = 2 + X₁ OA = {x₁ ≤ 2+ X₂UX ≤ 2+ X₁} Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = P(at least four) =

You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your​ study, you randomly select 3589 vehicle crashes and organize the resulting data as shown in the contigency table. At α=0.10​, can you conclude that the type of crash depends on the type of​ vehicle? Complete parts​ (a) through​ (d).   Vehicle   Type of crash Car Pickup Sport utility ​ Single-vehicle 866 323 340 ​ Multiple-vehicle 1145 487 428       Question content area bottom Part 1 ​(a) Identify the claim and state the null and alternative hypotheses.   H0​: The type of crash and the type of vehicle are ▼   independent dependent . Ha​: The type of crash and the type of vehicle are ▼   dependent independent .   The ▼   alternative hypothesis null hypothesis is the claim.

When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires. If X and Y are independent with p(0) = 0.5, p.(1) = 0.3, p (2) = 0.2, and p (0) = 0.1, p(1) = 0.6, p. (2) = P(3) = 0.05, p.(4) = 0.2, display the joint pmf of (X, Y) in a joint probability table. 白白白 P(x, y) 2 Compute P(X s 1 and Ys 1) from the joint probability table. P(X s1 and Y s 1) = Does P(X s1 and Ys 1) equal the product P(X s 1)· P(Y s 1)? O Yes O No What is P(X + Y = 0) (the probability of no violations)? PIX + Y = 0) = Compute P(X + Ys 1). P(X + Ys 1) =

WebAssign + → X CO TE ICTTET EER .... .... ...... H...... How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 26 retail stocks such as Toys 'R' Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity. The result was x1 = 13.6. A random sample of 33 utility (gas and electric) stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied for x2, profit as a percentage of stockholder equity. The result was x2 = 10.1. Assume that o1 = 4.2 and o, = 3.3. (a) Categorize the problem below according to parameter being estimated, proportion p, mean u, difference of means µ1 - µ2, or difference of proportions p1 - P2. Then solve the problem. O µ1 - 42 O p P1- P2 (b) Let µ̟ represent the population mean profit as a percentage of stockholder equity for retail stocks, and let u2 represent the population mean profit as a percentage of…

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A researcher designed a study to test whether caffeine use enhanced performance time to run a 100 meter sprint. The participants (n=30) ran a 100 meter sprint before the consumption of caffeine on day 1 and then they ran another 100 meter sprint on the following day 2 after ingesting caffeine. The average time taken to run the 100 meter sprint on day 1 was (M1) and the average to run on day 2 after caffeine was (M2). The variance for this study was calculated to be (S2).  Does caffeine use improve the running time in the 100 meter sprint (e.g., lower time)?  Use all of the data provided to you below and test at an alpha of 0.05. M1 = 26.53M2 = 14.69S2 = 207.75n=30 a) state null and alternate hypothesis b) what is the critical value  c) what is the obtained value  d) conclusion

Defective concrete on a construction site can be caused by either poor workmanship (selection and grading of material, pouring, curing) or poor aggregate, or both. The quality of the aggregate is affected by the quality of the workmanship, and vice versa. W = poor workmanship, A = poor aggregate On a given project: P(A) = 0.25 P(W | A ) = 0.33 P(A | W) = 0.18 What is the probability of poor workmanship, P(W), on the project to 3 decimal places?

A food manufacturer uses an extruder (a machine that produces bite-size cookies and snack food) that yields revenue for the firm at a rate of $200 per hour when in operation. However, the extruder breaks down an average of two times every day it operates. If Y denotes the number of breakdowns per day, the daily revenue generated by the machine is R = 1600 − 50Y 2. Find the expected daily revenue for the extruder.