# Question

For the transition matrix Q, prove that the equally likely source distribution, Pi = 1/3, i = 1, 2, 3, is the one that maximizes mutual information and hence the mutual information of the capacity associated with the channel described by Q.

## Answer to relevant Questions

Suppose X and Y are independent and exponentially distributed both with unit- mean. Consider the roots of the quadratic equation Z2 + Xz + Y = 0. (a) Find the probability that the roots are real. (b) Find the probability ...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). Let be a zero- mean Gaussian random vector with covariance matrix, Write out the joint PDF, fX, Y, Z (x, y, z). Show that the derivative of reduces to the form Let the random variables U, V, and W be as described. (a) Find the MAP estimator of U given the observation {V = v, W = w}. (b) Find the ML estimator of U given the observation {V = v, W =w}. (c) Find the LMMSE estimator ...Post your question

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