# Question: Starting from the general form of the joint Gaussian PDF

Starting from the general form of the joint Gaussian PDF in Equation (5.40), show that the resulting marginal PDFs are both Gaussian.

In Equation 5.40

In Equation 5.40

## Answer to relevant Questions

Starting from the general form of the joint Gaussian PDF in Equation (5.40) and using the results of Exercise 5.35, show that conditioned on Y = y, X is Gaussian with a mean of μx + ρXY (σX / σY) (y – μY) and a ...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) Given the joint characteristic function of a pair of random variables, Φ X, Y (ω1, ω2). How do we get a marginal characteristic function of one of the random variables, say, Φ X (ω) from the joint characteristic ...Let and be independent and both uniformly distributed over (0, 2π. Find the PDF of Z = (X + Y) mod 2π. Suppose M and N are independent discrete random variables with identical Poisson distributions, Find the PMF of L = M– NPost your question