Pr(H | E) \text{ is the probability that the the hypothesis } H \text{ is true given evidence } E \text{ is true} \\
Pr(H) \text{ is the probability that the hypthesis } H \text{ is true prior to } E \\
Pr(\neg H) \text{ is the probability that } H \text{ is false prior to } E \\
Pr(E\vert H) \text{ is the probability ) E \text{ is true given } H \text{ is true} \\
Pr(E\vert\neg H) \text{ is the probability } E \text{ is true given } H \text{ is false} \\

M_X(t) &= \int_{\mathbb{R}} e^{tx} f(x) dx \\
       &= 2 \int_{0}^{\infty} e^{(t - 2) x} f(x) dx \\
       &= 2 \frac{1}{t-2} e^{(t-2)x} |{0}^{\infty} \\
       &= \frac{2}{t - 2} e^{(t-2)x} |{0}^{\infty} \\
       &= \frac{2}{2 - t}; t \in (-\infty,2)