Suppose we have a joint PMF of a random vector (X, Y)T: Sie cos(x), 0< r < , 0
Q: Please show step by step answer and calculate everything and make the graphic also.
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A: False
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- C2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition of covariance, show that Cov(aX, Y): = a Cov(X, Y). You may find it helpful to remember that if EX = µx, then EaX = αμχ· (b) Show that Cov(X + b, Y) = Cov(X, Y). Now let X, Y, Z be independent random variables with common variance o². (c) Find the value of Corr(2X - 3Y + 4, 2Y – Z - 1). You may use any facts about covariance from the notes, including those from parts (a) and (b) of this question, provided you state them clearly.Let Z₁ = X₁-HX σχ N(0,1), and W₁ = ~N(0,1), for i = 1,2,3,...,10, then: Y₁-Hy OY iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4.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) :
- Q. 5 Let X be a continuous uniform random variable on [-a, a]. Find the pdf for Y = g(X), where 0, x b. g(x) = 3x,Q2) The joint probability function of two discrete random variables X and Y is given by fx,y) = c(2x+y),where x and y can assume all integers such that 0 sIS2,0s ys3,and fx,y) = 0 otherwise. (a) Find the value of the constant c (b) Cov (X, Y), (c) p.Let X and Y be random variables with joint den- √(x+2y) x,y>0,x+y Y). (b) Calculate fx y(xly). sity: f(x,y): = (c) Calculate P(X < 1 Y = 1). (d) Calculate E[X²|Y].
- Which of the following is false for continuous and independent random variables Y and Z?The joint pdf of the random variables X and Y is given by { cx, x > 0, y > 0, 1 < x + y < 2, f (x, y) 0, elsewhere, for some constant c. (a) Draw the support of (X, Y). (b) Show that c= = 6/7.Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. FInd (d) fZ|XY (z|x,y), (e) fX|YZ(x|y, z).