What is the expression of the joint PDF of X and Y in the region {(x, y) : 0 ≤ y ≤ x² < 1}? What is the expected value of X? What is the expected value of Y?
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- Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.Let random variable X be uniform in the interval (0, 1). Define random variable Y = aX + b where a not 0.Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.
- A point (X, Y) is selected at random inside a region defined by {(x, y): 0 ≤ y ≤ x² ≤ 1}. Assume that the point is equally likely to fall anywhere inside the region. What is the expression of the joint PDF of X and Y in the region {(x, y): 0 ≤ y ≤ x² < 1}? What is the expected value of X? What is the expected value of Y? What is the covariance of X and Y?2) Let X be a continuous random variable with PDF 0Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by Sk(6–x), 0Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 0A random point is chosen inside the unit square {(x ,y ) : 0 <= x,y <= 1}. What is the expected value of the distance from this point to the point (0,0)?Let X be a continuous random variable with PDF (2e*,0 /3).Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf f(x, y) = K(x2 + y2) 19 ≤ x ≤ 29, 19 ≤ y ≤ 29 0 otherwise (a) Determine the conditional pdf of Y given that X = x. fY|X(y|x) = for 19 ≤ y ≤ 29 Determine the conditional pdf of X given that Y = y. fX|Y(x|y) = for 19 ≤ x ≤ 29 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = 3 350,600 . Round your answer to three decimal places.) Compare this to P(Y ≥ 25). (Round your answer to three decimal places.)P(Y ≥ 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = 3 350,600…SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,