Question: 89. A DNA sequence can be represented as a sequence of letters, where the alphabet has 4 letters: A,C,T,G. Suppose such a sequence is generated

89. A DNA sequence can be represented as a sequence of letters, where the alphabet has 4 letters: A,C,T,G. Suppose such a sequence is generated randomly, where the letters are independent and the probabilities of A,C,T,G are pA, pc, pr, pa, reapectively. (a) In a DNA sequence of length 115, what is the variance of the number of occurrences of the letter C? (b) In a DNA sequence of length 115, what is the expected number of occurrences of the expression CATCAT? Note that, for example, the expression CATCATCAT counts as 2 occurrences. (c) In a DNA sequence of length 6, what is the probability that the expression CAT occurs at least once

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