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Could you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of
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- Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table. Find: 1) The Covariance Cov(X,Y)? (Cov(X,Y) = MxY-MxMY) 2) The correlation (pxy) between X and Y where Pxy = Cov(X,Y) PXPY Y 3 fx(x) f(x,y) 1 2 1 1/4 1/4 0 X 2 0 1/4 1/4 fy(y) Note that 2 n=2 n=3 Px² = Σn²±²x² f(x, y) - μ and py² = Σ3y² f(x, y) – µ Zk=0Suppose that X and Y have a joint probability density function given by Sce-3-5y 10 if a, y 20 fx.x(x, y) = otherwise Find the conditional probability density function fyjx=z·2. Let f(x, y) be the probability density function of the continuous random variable (X, Y). If U = XY, show that the probability density function of U is given by fu(u) = [ƒ€.) | dv. ( , v) |
- Let X and Y be two continuous random variables with joint probability density function: 6e-(2x+3y)+k x21, y > 0 fxy (x, y) = otherwise a) Find the coefficient k. b) Find P(X 2). c) Find the marginal probability density functions of X and Y ( fx(x), f;(y)). d) Are X and Y independent?Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.The joint density of X and Y is given by, ху, Iw(x, y) = (x² +: 0 l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y2. Let X and Y have the joint density given by: f(x, y) = k(2x+y) for 0 < x, y < 1 0 otherwise where k is a constant. Find k. Also, obtain the conditional density, conditional mean and conditional variance of Y given X = ½ (14 pointelSuppose that X and Y have a joint probability density function given by: ( only for D) and E), ignored A),B)and C))1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 03. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage