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3. Gaussian Mixture Distribution Let iii, of.) 1 g i g ill-f, be a xed set of constants. Let 6' be a discrete random variable taking on values 91-, 1 g '5 g ill/I= with respective probabilities 1'1}, 1 g i g M'. Assume X |9 = 19;; N N (m, of). This means the conditional distribution of X given 6) = 6% is Gaussian with mean its; and variance 0?. (3.) Find the (unconditional) pdf of X , f (:5). The distribution of X is called a Gaussian mixture. (b) Is the conditional distribution 6|X discrete or continuous? write the prof 39 (at) or pdf f (6|x), whichever is appropriate. This must be an EXPLICIT formula, though it does not have to be simplied