BBy Bot
Jun 09'24
Exercise
[math]
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- Show that for [math]m \ge 1[/math],
[[math]] f_{2m} = u_{2m-2} - u_{2m}\ . [[/math]]
- Using part (a), find a closed-form expression for the sum
[[math]] f_2 + f_4 + \cdots + f_{2m}\ . [[/math]]
- Using part (b), show that
[[math]] \sum_{m = 1}^\infty f_{2m} = 1\ . [[/math]](One can also obtain this statement from the fact that[[math]] F(x) = 1 - (1-x)^{1/2}\ .) [[/math]]
- Using parts (a) and (b), show that the probability of no equalization in the first [math]2m[/math] outcomes equals the probability of an equalization at time [math]2m[/math].