A binary source generates a sequence of symbol with probabilities p and 1-p, respectively. Given the first

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Question:

A binary source generates a sequence of symbol with probabilities p and 1-p, respectively. Given the first symbol in the sequence, the source continues to generate symbols until the opposite symbol is generated. Let X note the length of the sequence, including the first symbol.

a) Find the probability mass function of X.

b) Find the expected value of X.