have The following pattern classes Gaussian probability density functions : w, = {(0, 0)", (2, 0)", (2, 2)*, (0, 2)4 and %3D 1 W2 = {(4, 4)", (6, 4)*, (6, 6)', (4, 6)*1. Assume that P(w,) = P(w,) = 1 and 2 %3D obtain the equation of the Bayes' decision boundary between these two classes. Also, sketch the boundary.

You are given the probability distribution function (PDF) of a continuous random variable X is fX(x). Let Y be a continuous random variable such that Y = aX + b, where a and b are non-zero real constants.1. Find the PDF of Y in terms of  fX , a, and b.2. Let X be an exponential random variable with parameter λ. When will Yalso be an exponential random variable? 3. Let X be a normal random variable with mean μ and variance σ2 . Whenwill Y also be a normal random variable?

question d and e