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The random variable $X$ has mass function

$p(x) = \begin{cases} \frac{1}{10} & x=0 \\ \\ \frac{3}{10} & x=4 \\ \\ \frac{3}{5} & x=6 \end{cases}$

Provide your answers to two decimal places.

(a) Find the moment generating function of $X$ and evaluate it at the point $t$ =.

(b) Find the second derivative of the moment generating function and evaluate it at the point $t$ =.

(c) Use the m.g.f. to find the second moment of $X$ .

You can earn partial credit on this problem.