Let X be a discrete random variable. The moment generating function of X is given by
Mx(t) = (1 - 0.9 + 0.9et)15 = (0.1 + 0.9et)15
The first moment of X is given by differentiating MX(t) once at t = 0.
M'X(t) = (0.1 + 0.9et)15
= 15 * (0.1 + 0.9et)14 * 0.9et
= 13.5et * (0.1 + 0.9et)14
So, M'X(0) = 13.5e0 * (0.1 + 0.9e0)14
= 13.5 * 1 * 114
= 13.5
Therefore, the first moment of X is 13.5
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