Verify the formula for the moment generating function of a uniform random variable that is given in Table 7.2. Also, differentiate to verify the formulas for the mean and variance.

Table 7.2

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Probability density function, f(x) Moment Mean generating function, M(t) Uniform etb - eta a + b a 0 s-1 (de-d*(2x)*¯ r(s) Gamma x 20 え with f(x) = parameters x< 0 (s, 1), 1> 0 Normal - 0