# Question

Let θ be a phase angle which is uniformly distributed over (0, 2π. Suppose we form two new random variables according X = cos (aθ) and Y = sin (aθ) to and for some constant a.

(a) For what values of the constant are the two random variables X and Y orthogonal?

(b) For what values of the constant are the two random variables X and Y uncorrelated?

(a) For what values of the constant are the two random variables X and Y orthogonal?

(b) For what values of the constant are the two random variables X and Y uncorrelated?

## Answer to relevant Questions

Consider again the joint CDF given exercise 5.3. (a) For constants a and b, such that 0 < a < 1, 0 < b < 1 and a < b, find Pr (a < X < b). (b) For constants and, such that, 0 < c < 1, 0 < d < 1 and c < d, find Pr (c < y < ...Two fair dice are rolled. Let one of the dice be red and the other green so that we can tell them apart. Let be the sum of the two values shown on the dice and be the difference (red minus green) of the two values shown on ...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 ...A quarterback throws a football at a target marked out on the ground 40 yards from his position. Assume that the PDF for the football’s hitting the target is Gaussian within the plane of the target. Let the coordinates of ...Let and be independent zero- mean, unit- variance Gaussian random variables. Consider forming the new random variable U, V according to U = [X] cos(θ) –[Y ] sin(θ) V = [X] sin (θ – [Y] cos (θ).Post your question

0