The random variables X and Y have joint pdf (x(1+3y²) fxy (x, y) = 0 < x < 2, 0< y < 1 4 0, otherwise
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- you are analyzing the variables that explain the returns on the stock of the Boeing Com- pany. Because overall market returns are likely to explain a part of the returns on Boeing, you decide to include the returns on a value-weighted index of all the companies listed on the nySe, aMeX, and naSdaQ as an independent variable. Further, because Boeing is a large company, you also decide to include the returns on the S&P 500 index, which is a value-weighted index of the larger market-capitalization companies. Finally, you decide to include the changes in the uS dollar’s value. to conduct your test, you have collected the following data for the period 1990–2002. Rt = monthly return on the stock of Boeing in month t RALLt = monthly return on a value-weighted index of all the companies listed on the nySe, aMeX, and naSdaQ in month t RSPt = monthly return on the S&P 500 index in month t ΔXt = change in month t in the log of a trade-weighted index of the foreign exchange value of the uS…3. Let X, Y be continuous random variables with joint pdf f(x, y). Calculate the joint cumulative distribution function of (X, Y) for each of the pdfs below. (a) f(x, y) = 6e-³x-2y, x, y ≥ 0. (b) f(x, y) = x + ³y², 0 ≤ x, y ≤ 1.A continuous random variable X has the PDF fx(x)=kx2, 0 < ? < 1.a) What is the value of k ?b) Find the variance of Xc) What is the value of m so that P[X<=m] = 1/2 ?d) Find the PDF of the new random variable Y obtained from X through the lineartransformation Y=4X+1.
- 8. (Same as #4) At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's capacity that is sold in the same week. The joint pdf of X and Y is given by f(x,y) (3x if 0 ≤ y < x < 1 = 0 otherwise a) Find the marginal probability distributions of X and Y. b) Show that the two random variables are not independent. Using part of your answer to a) is a much shorter solution. Once you've done this with probability, using common sense is VERY straightforward.Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2Let X and Y be random variables for which the joint PDF is as follows: (8xy f(x, y) = {8xy for 03. Let X, Y be continuous random variables with joint pdf f(x, y). Calculate the joint cumulative distribution function of (X, Y) for each of the pdfs below. (a) f(x, y) = 6e-3x-2y, x, y ≥ 0. (b) f(x, y) = x + ³y²,0 ≤ x, y ≤ 1.(16) The moment-generating function of the geometric random variable X with parameter p is M(t) = 1-per. Use this to find the mean and variance of X.3. Consider two random variables X₁ and X2 whose joint pdf is given by for x₁0, x2 > 0, x₁ + x2 < 2, { Find the pdf of Y = X₂ - X₁. f(x1, x₂) = NIT otherwise.The joint PDF of two jointly continuous random variables X and Y is S c(x2 + y?) for 0 < x < 1 and 0 < y < 1, fx,x(x, y) ‚Y otherwise. c = 3/2. E(Y) = 5/8. 3(2X2 + 1) 4(3X² + 1)' Show that E(Y|X) :The joint PDF of a two dimensional random variable (X, Y) is given by x? f(x, y) = xy +– 01) (ii) P(y 1 /y 1) (v) P(xattached belowSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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