# Question: A pair of random variables has a joint PDF specified

A pair of random variables has a joint PDF specified by

fX, Y( x, y) = d exp (–( ax2+ bxy+ cy2))

(a) Find the constant in terms of a, b, and c. Also, find any restrictions needed for a, b, and c themselves for this to be a valid PDF.

(b) Find the marginal PDFs, fX (x) and fY (y).

(c) Find Pr (X > Y).

fX, Y( x, y) = d exp (–( ax2+ bxy+ cy2))

(a) Find the constant in terms of a, b, and c. Also, find any restrictions needed for a, b, and c themselves for this to be a valid PDF.

(b) Find the marginal PDFs, fX (x) and fY (y).

(c) Find Pr (X > Y).

## Answer to relevant Questions

A pair of random variables has a joint PDF specified by a) Find the constant c. b) Find Pr (X2 + Y2 > 1 / 4). c) Find Pr (X > Y). A vector random variable, X has a covariance matrix and a correlation matrix given by Find the mean vector, E [X]. 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 ...A set of random variables, X1, X2, X3, Xn, are independent and each uniformly distributed over ( 0, 1). (a) Find the probability density function of Z = max(X1, X2… Xn). (b) With defined as in part (a) above, let A be ...Suppose X, Y, and Z are jointly Gaussian random variables with mean vector and covariance matrix given by Find Pr (X > 2Y – 3X).Post your question