In Euclidean spaces, a set C is called a convex set if for all x and...

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In Euclidean spaces, a set C is called a convex set if for all x and y in C, the line segment connecting x and y is included in C. In other words, the affine combination tx + (1 - t)y belongs to C, for all x, y = C, and t = [0, 1]. Prove that if a Markov Chain has stationary distribution, then all stationary distribution of this Markov Chain is a convex set. In Euclidean spaces, a set C is called a convex set if for all x and y in C, the line segment connecting x and y is included in C. In other words, the affine combination tx + (1 - t)y belongs to C, for all x, y = C, and t = [0, 1]. Prove that if a Markov Chain has stationary distribution, then all stationary distribution of this Markov Chain is a convex set.

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To prove that the set of stationary distributions of a Markov chain is convex let ... View the full answer