2) The joint density of X and Y have the joint density function f(x,y) = { cx(2-x-y), 0 < x < 1, 0, 0x1, 0 < y < 1 otherwise. (a) Find the constant c. (b) Compute the condition density of X, given that Y = y, where 0 < y < 1.
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Find Mx, My and (x, y) for the lamina of uniform density p bounded by the graphs of the equations. Mx = My (x, y) = = -x² + 3x + 6, y = x + 6 y = -Let f(x, y) = e "-Y 0 < x < ∞, 0 < y < ∞ be the joint pdf of X and Y. Find the pdf and cdf of X and Y.
- x(1+3y°) f (x, y) = - 0II. Let RVsx, Y be uniform on triangle with vertises (0, 0), (2, 2), (2, 2). Find 1. Joint pdf 2. Marginal pdfs 3. P(Y > 1 x > 0) 4. Cov(x, Y) III. Let RVY = x + N where x = B(1,1/3) and N = N(2, 3) are independent. Consider vector RV V = (xY)T. Find E(V) = and covariance matrix KV IV. Let U = 2x, V = X + Y, and W = 3X + 3Y - Z, where X, Y, Z are independent standardGaussian.1. Find joint pdf for U, V, W 2. Find marginal pdf fV (V)Let F (x, y, z) = 22 y ³ x5 What is the value of div F at (1, 2, 3)?Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape. p = 6 Mx = My = (X, y) =| (6, 5) yA Enhanced Feedback Please try again, keeping in mind that the center of mass (x, y) is given by x = My and y = Mx. Remember that My = p x[f1(x) – f2(x)]dx and Mx = p PIfi(x)1? - [f2(x)]²} dx, where fi(x) z F2(x). Write a function for the line passing the origin and the m igiven point. Need Help? Read It Watch It Submit AnswerThe velocity field of a fluid v (in meters per second) has divergence div(v)(P) = 6 at the point P = (8, 4, 2). Estimate the flow rate out of the sphere of radius 0.2 centered at P. (Use decimal notation. Give your answer to four decimal places.) flow rate: