ata Y are independent random variables with density functions Jx (x) = e* . u (x) and fy (y) = 2 - e-2y u (y), find the density function of X +X= Z
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- Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),Use the transformation technique to find the density function for the random variable Y. The density function should be given as a piecewise function. f(x) = 1/3e^-1/3x x>0 Y=e^x 0 elsewhere
- Two non-negative random variables X and Y have a joint density function f(x, y) = re-*v +1) x > 0, y > 0 Find the correlation coefficient.• Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1, +1).A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is given by: (ay“ if y> yo fV) = ya+T (0, elsewhere i) Derive the mean of Y. Show all necessary steps. ay (a-2)(a-1)²' ii) Show whether or not that the variance of Y is ·
- Let Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal toLet X and Y be two independent random variables with respective probability density functions (pdfs) 0, x 0 ue-HY, y > 0 The expression for P(X > 1, Y < 1) is Select one: о (1-е ^) . е и O ed. e H O (1 - e ") · e-A O A. µ.e-de 4Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
- The joint probability density function of two dimensional random variable(X,Y) is given 8 by f(x, y) = xy, 13xsys2 9 = 0, elsewhere Find the marginal density functions of X and Y.Let X and Y be continuous random variables having a joint pdf given by f(x, y) = e-*, 0sysx 3).Let f(x) is density function of continuous random variable x then the (expected value E(x Ek) = [ xfx)dx Ew) = [_fx)dx - 00 Ek) = ] -xfx)dx Ex)= | xf(x)dx