5) Consider the random variable X and Y that represent the number of vehicles thatarrive at two separate street corners during a certain 2-minute period. These streetcorners are fairly close together so it is important that traffic engineers deal with themjointly if necessary. The joint distribution of X and Y is known to bef(x, y) =91614(x+y)'for x = 0, 1, 2,... and y = 0, 1, 2, ....(a) Are the two random variables X and Y indepen-dent? Explain why or why not.(b) What is the probability that during the time pe-riod in question less than 4 vehicles arrive at thetwo street corners?

Answered: Image /qna-images/answer/605e7a47-7328-48ca-8880-f0a4ebeed641.jpg

Answered: 5) Consider the random variable X and Y…

A First Course in Probability (10th Edition)

10th Edition

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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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IT HAS BEEN FOUND THAT A FLUCTUATING ELECTRIC CURRENT X AT ONE OF THE ESKOM SUBSTATIONS HAS A UNIFORM PROBABILITY DISTRIBUTION, f(x) = a≤x≤b otherwise a+b (b-a)² WITH E(X) = AND Var (X) = 12 AS THE STATISTICIAN AT ESKOM AND HAVE BEEN GIVEN A RANDOM SAMPLE OF 7 MEASUREMENTS X₁, X₂,,X, OF THE ELECTRIC CURRENT TO INFER ABOUT THE MEAN FLUCTUATION OVER A SPECIFIC PERIOD. AFTER CAREFUL CONSIDERATION YOU HAVE IDENTIFIED THREE POSSIBLE ESTIMATORS 0₁ = X₁+X7, 0₂ = X₁ +2X₂+X AND 3 = X 3 Show which of the estimators possess this property
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7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
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