tabRules for expectation and variance of random variablesSuppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space.Suppose that we also have the following.E(X)=-7Var (X)=9E(Y) = 4E(Z)=1Var (Y)=30 Var (Z)=7Compute the values of the expressions below.EE(-2Y-4)= 0-5X-4ZVar (2X-1)=E (22²) = 0Explanationesc!QCheck@2WX#3E$4%R5MacBook ProFr^H6Ⓒ2022 McGraw Hill LLC. All Rights22.&Y8UH Charmaine has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the San Bernardino Freeway, and the other is to go viathe Pomona Freeway. Recently, a lane was added to the San Bernardino Freeway. So, Charmaine wants to determine if it is now faster to take the SanBernardino Freeway than the Pomona Freeway. She selected a random sample of 12 of her trips via the San Bernardino Freeway and a random sample of 12 ofher trips via the Pomona Freeway. The two samples were chosen separately, so that the selection of the trips via the San Bernardino Freeway did not affect theselection of the trips via the Pomona Freeway. Charmaine recorded the travel times (in minutes) for the trips in each of the two samples. The following tablegives the data, sample means, and sample standard deviations.O independent samplesO paired (dependent) samplesTravel times in minutesS.B. Fwy 79, 76, 66, 69, 71, 75, 67, 75, 65, 60, 76, 74Pomona Fwy 63, 76, 79, 78, 74, 71, 65, 75, 65, 71, 77, 71Send data to calculator(a) Are the two samples of trips independent or paired (dependent) samples? Choose the best answer.Oz= 00t=ExplanationSample mean Sample standard deviationSCheck71.1(b) Charmaine wants to use the data to determine whether the mean travel time via the San Bernardino Freeway is less than the mean travel time via thePomona Freeway. Assume that both populations are approximately normally distributed and that the population variances are equal.72.1Choose the appropriate test statistic for the hypothesis test that would be performed. Then calculate that statistic. Carry your intermediatecomputations to three or more decimal places. Round your answer to three decimal places. (If necessary, consult a list of formulas.)MacBook Pro5.75.4&.6**Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Cent

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. Е (x) -0 Var(X) = E(Y)=-7 E (Z) = 4 = 42 Var(Y) = 39 var(Z)= Compute the values of the expressions below. E (4Y-1) = 0 믐 ? (2) - n E -1-Var(r) = 0 %3D E (2x*) = 0 olo
Can help explain why the other options are correct and why this option is incorrect? Thank you!
Q6. For two random variables X and Y, fxy(x, y) = 0.5 8(x+1) &(y)+0.1 8(x) 8{y) + 0.1 8(x) 8(y-2) + 0.4 &(x-1) S(y+2) + 0.2 &x– 1) d(y – 1) + 0.5 8(x – 1) 8(y – 3). Find, (a) The correlation
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X = 2N−2N2 - 1. The values of X are given in the table below. Outcome ttt hht tth htt hhh tht hth thh Value of X −1 −5 −1 −1 −13 −1 −5 −5 Calculate the probabilities P (X = x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P (X = x)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-9 E (Z) = 1 E (Y)=-6 Var(Y)=28 Var(Z) = 47 Var (X)=44 Compute the values of the expressions below. E (2-Z) = 0 E(X+32)=0 -5 -2-Var(4X) = 0 E(-x²) = 0 Continue □ X S M 31 Ⓒ2022 McGraw Hill LLC. All Rights Reserved
3. Let X₁, X2,..., Xn be iid random variables with mean and variance o2. Define the random variable X-L Z o/√√n where X = (X₁ + X2 + ... + Xn). Find the mean and variance of Z.
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (1) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is htt, then N (htt) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N-N2 -4, The values of X are given in the table below. Outcome hht tth hth thh tht ttt hhh htt Value of x -4 -3 -4 -4 -3 -4 -7 -3 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value of x _ _ _ p(X=x) _ _ _
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-6 E(Y)=-9 E(Z)=3 Var (X)=8 Var (Y)=14 Var (Z)=25 Compute the values of the expressions below. E (-1- 37) - I -2x - 5z 4 Var (47) - 2 - I e(32°) - [I Dlo
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N² -6N-1. The values of Xare given in the table below. Outcome thh tth hhh hth ttt htt hht tht Value of X -5 -5 − 1 -5 −1 -5 -5 -5 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 8 X
Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are constant random variables.
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=0 Var(X) = 39 Var(Y) = 19 Var(Z) =24 E(Y) =-4 E(Z)=6 Compute the values of the expressions below. E(1+5z) = -Y-4Z E 2 Var(4–3Y) = I E(sz²) = I

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