The two random variables and Y have the joint density function: c, 0<2y
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A: Hi! Thank you for the question , As per the honor code , we are allowed to answer three sub-parts at…
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- Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.The random vector (X, Y) has the following joint probability density function: e-(2²+y²) , x > 0, y > 0, otherwise 4rye S(x.x)(x, v) = { Let Z = VX? +Y² . Find the probability density of the random variable Z.2. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 0Two continuous random variables Y₁ and Y₂ has the joint density function if y₁ > 0, Y2 > 0, Y1 +Y2 < 2; { otherwise. f(y₁, y2) = y2, Y2 0. a) Are Y₁ and Y2 independent? Verify your answer. b) Find the conditional pdf f(y2|y₁). c) Find Cov(Y1; Y2).Q 4.2. Let (X, Y) be a random variable with the following density: {152-2 0 £x,x (x, y) = { 1. Express E(Y|X) in terms of X. 2. Express Var(XY) in terms of Y. 0 < x < y < 1, otherwise.b) Let X and Y be jointly continuous random variables with the following joint density function (1/32)xy ,0 2) v. Evaluate P(Y > X – 2)Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0The joint probability function of random variables X and Y is given to be: 3x- y 15x<41Suppose X and Y are independent random variables. X iş uniformly distributed on (0,) and Y is exponentially distributed with 1=2. Find the joint density function f(x, y) of X and Y.Find the density of U = Y1 +Y2, where Y1 and Y2 are independent random variables with densities (yı – 1), 3 < Yı < 4, (y2 + 2), 0 < Y2 < 1, fy, (y1) : fy,(y2) = otherwise, otherwise.The value of the random variable X is from the unit disc D {(x, y) | < 1}distance of a randomly chosen (ie density function = constant x² + y² = 1/A) point from the origin. Calculate its expected value EX = = = √ √ √₁₂ √x² + y² dA. =Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON