which is to say that Sn() = X1() + X2() + + Xn(). Clearly, Sn is the total number of heads which

which is to say that Sn(ω) = X1(ω) + X2(ω) + · · · + Xn(ω). Clearly, Sn is the total number of heads which occur, and Sn takes values in {0, 1, . . . , n} since each Xi equals 0 or 1. Also, for k = 0, 1, . . . , n, we have that P(Sn = k) = P

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{ω ∈  : h(ω) = k}

=

X

ω: h(ω)=k P(ω)

=



n k