Consider a discrete memory less source with source alphabet

Consider a discrete memory less source with source alphabet

Consider a discrete memory less source with source alphabet L {s0, s1,. . . , sk–1) and source statistics (p0, p1, … pk–1,) The nth extension of this source is another discrete memory less source with source alphabet Ln’ = {s0, s1, .., sM – 1), where M = Kn. Let P(si) denote the probability of si.
(a) Show that which is to be expected.
(b) Show that where pik is the probability of symbol sik, and H(L) is the entropy of the original source.
(c) Hence, show that

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