# Question

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

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