# Question: For positive constants and a pair of random variables has

For positive constants and, a pair of random variables has a joint PDF specified by .

Fx, y (x, y) = abe-(ax = by) u (x) u (y)

(a) Find the joint CDF, Fx, y (x, y).

(b) Find the marginal PDFs, fx (x) and fy (y).

(c) Find Pr (X > Y).

(d) Find Pr (X > Y2).

Fx, y (x, y) = abe-(ax = by) u (x) u (y)

(a) Find the joint CDF, Fx, y (x, y).

(b) Find the marginal PDFs, fx (x) and fy (y).

(c) Find Pr (X > Y).

(d) Find Pr (X > Y2).

## Answer to relevant Questions

Suppose and are independent, Cauchy random variables with PDFs specified by Find the joint PDF of Z = X2 + Y2 and W = XY Suppose Z = X + jY is a circular Gaussian random variable whose PDF is described by Equation (5.70), (a) Find the PDF of the magnitude, R = |Z|, and phase angle, θ =∠ Z, for the special case when μZ = 0. (b) Find the ...Suppose X and Y are independent and exponentially distributed both with unit- mean. Consider the roots of the quadratic equation Z2 + Xz + Y = 0. (a) Find the probability that the roots are real. (b) Find the probability ...Let X = [X1, X2….Xn] T be a vector of random variables where each component is independent of the others and uniformly distributed over the interval. (a) Find the mean vector, E [X]. (b) Find the correlation matrix, Rxx ...Let X = [X1, X2, X3] T represent a three- dimensional vector of random variables that is uniformly distributed over a cubical region (a) Find the constant c. (b) Find the marginal PDF for a subset of two of the three random ...Post your question