The joint density function of the continuous random variables X and Y is expressed below. Find: (a) the value of the constant c, (b) P(X < 0.5, Y > 0.2). cx2 (y+1)3, for 0.2 < x < 0.7, 0.1 < y < 0.5, [cx² (y f(x, y) = 0, otherwise
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- Suppose that Y is a continuous random variable. Show EY yfr(y)dy.Let X and Y be jointly continuous random variables with joint PDF cx +1, 2,y> 0, x+ y<1 0, fx,x (x, y) = otherwise. Then the constant c= And the probability that P(Y < 2X²) = ;: Here a = and b =Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
- Show complete solution: Assume that X and Y are independent random variables where X has a pdf given by fx(x) = 2x1(0,1) (x) and Y has a pdf given by fy(y) = 2(1 — y)I(0,1)(y). Find the distribution of X+Y.Let X and Y be random variables such that var(X) = and p = 16, var (Y) = 9, cor (X, Y) = -0.5. a. Find var(2X – 2Y + 10), b. Find cov(X – Y, X +Y).1. A continuous random variable X is defined by (3+x) f(x) - 3 sxs- 1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean II
- The continuous joint random variables (X, Y, Z) have the joint pdf ƒ (x, y, z)= a, for 0 0. Write this pdf using the indicator function (1)(x)=1, if sAssume that X and Y are independent random variables where X has a pdf given by fx(x) = 2aI(0,1)(x) and Y has a pdf given by fy(y) = 2(1– y)I(0,1)(y). Find the distribution of X + Y.Let the random variables x and y have joint pdf as follows: f(x,y) = (11x² + 4y²), 0Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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