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The random variable $X$ has moment generating function

$\phi_{X}(t) = \left( 0.26 e^{t} + 1 - 0.26 \right)^{14}$

Provide answers to the following to two decimal places

(a) Evaluate the natural logarithm of the moment generating function of $2 X$ at the point $t=0.87$ .

(b) Hence (or otherwise) find the expectation of $2 X$ .

(c) Evaluate the natural logarithm of the moment generating function of $2 X + 9$ at the point $t=0.87$ .

You can earn partial credit on this problem.