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Do the following problems: a. Use mathematical induction to show that 1 + 2 + 22...

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Advance Math

Do the following problems:

a. Use mathematical induction to show that 1 + 2 + 22 +···+ 2n =2n+1 ? 1 for all non-negative integers n.
b. A coin is weighted so that P(H) = 2/3 and P(T) = 1/3. The coinis tossed 4 times. Let the random variable X denote the number ofheads that appear. (x) Find the distribution of X; (xx) Find theexpectation E(X).
c. Show a derivation of Bayes’ Theorem

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