Let X equal the number of flips of a fair coin that are required to observe...

  

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Let X equal the number of flips of a fair coin that are required to observe heads on consecutive flips. Let F equal the nth Fibonacci number where f = 1, f2 = 1, and fn fn-1+fn-2 for n = 3, 4, 5,... Then the p.m.f. of X is f(x) fx-1 = x=2,3,4,... Write down the equation for the moment generating function M(t) for this problem. Cal- culate the first four terms in the expansion. Let X equal the number of flips of a fair coin that are required to observe heads on consecutive flips. Let F equal the nth Fibonacci number where f = 1, f2 = 1, and fn fn-1+fn-2 for n = 3, 4, 5,... Then the p.m.f. of X is f(x) fx-1 = x=2,3,4,... Write down the equation for the moment generating function M(t) for this problem. Cal- culate the first four terms in the expansion.