Consider the following random experiment: A fair coin is tossed once. Here, the sample space has only two elements S = {H,T}. We define a sequence of random variables X₁, X₂, X₃, ⋯ on this sample space as follows:

a. Are the X_i's independent?

b. Find the PMF and CDF of X_n, F_Xn(x) for n = 1, 2, 3,⋯.

c. As n goes to infinity, what does F_Xn(x) look like?

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Xn(s) = n+1 1 if s = H if s = T