2. An information source produces binary triplets {000, 111,010, 101, 001, 110, 100, 011} with corresponding prob- abilities (1/4, 1/4, 1/8, 1/16, 1/16, 1/16, 1/16). A binary code assigns a codeword of length - log₂ Pk to triplet k. Let X be the length of the string assigned to the output of the information source. (b) Find the pmf of X.

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