Let X equal the number of independent tosses of a fair coin that are required to observe heads on consecutive tosses. Let u_n equal the nth Fibonacci number, where u₁ = u₂ = 1 and un = u_n−1 + u_n−2, n = 3, 4, 5, . . . .

(a) Show that the pmf of X is

(b) Use the fact that

to show that Σ^∞_x=2 p(x) = 1.

Transcribed Image Text:

p(x) = Uz-1 22 x = 2, 3, 4, ....