Let and be zero mean jointly Gaussian random variables with a correlation coefficient of and unequal variances of 2X and 2Y (a) Find the joint characteristic function, X, Y (1, 2) (b) Using the joint characteristic function, find the correlation, E XY (c) Find E X2Y2 ...

a Characteristic function of the jointly distributed Gaussian We know that condit ...

Let and be zero- mean jointly Gaussian random variables with a correlation coefficient of and unequal variances

Question:

Let and be zero- mean jointly Gaussian random variables with a correlation coefficient of and unequal variances of σ2X and σ2Y.
(a) Find the joint characteristic function, Φ X, Y (ω1, ω2).
(b) Using the joint characteristic function, find the correlation, E [XY].
(c) Find E [X2Y2].