A certain market has both an express checkout line and a super-express checkout line. Let X₁ denote the number of customers in lineat the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkoutat the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table.X2012300.08 0.08 0.040.0010.05 0.130.05 0.06X120.050.04 0.10 0.0630.000.03 0.04 0.074 0.00 0.01 0.05 0.06The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkoutis X1 X2. Calculate the expected difference.-

Step 1: Recall that E[X1-X2]=E[X1]-E[X2] due to linearity of expectation. Step 2: We just need to…

Answered: A certain market has both an express…

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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A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99
Exercise 1. Suppose that X - f(x) =÷1(x = 1,2,3,4,5). Compute... (a) E(X), (b) E(X²), and (c) E(X+2)² Hint: (X + 2)2 = X² + 4X + 4
1. Test whether the following expression is a valid CDF. The range of validity of the variable is 0 to ∞. If it is a valid CDF, obtain the corresponding pdf and its mean. If it is not a valid CDF, test whether it is a valid pdf? If it is a valid pdf, obtain the corresponding CDF and the mean. 2x x² A(x)-[1-exp(-) ++ [¹-exp(-²3)] -+-)] = exp 5 16 x² 8
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A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X, and X, is as given in the accompanying table. X2 1 3 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 X1 0.05 0.04 0.10 0.06 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.05 (a) What is P(X, = 1, X, = 1), that is, the probability that there is exactly one customer in each line? P(X, = 1, X, = 1) = | (b) What is P(X, = x,), that is, the probability that the numbers of customers in the two lines are identical? P(X, = X,) = (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 X, and X,. O A = {X, 2 2 + X2U X, 2 2 + Xq} O A = {X, s 2 + X2 U Xq 2 2 + Xq} O A = {X, s 2 + X2 U Xq S2+ Xq} O A = {X, 2 2 + X2 U Xq S2+ Xq} Calculate…

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