3. Let X be a discrete random variable and let Mx(t) be its moment-generating function. Define Rx(t) = In(Mx(t)). (a) Show that Rx(0) = 0. (b) Show that R'x(0) = E(X). (c) Show that RK (0) = V(X). (d)...

M-5 Please I need help with this question needed very clearly and step by step explanation and NEEDED ONLY TYPED SOLUTIONS PLEASE NO HANDWRITTEN please, will be really appreciated for your help.

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Extracted text: 3. Let X be a discrete random variable and let Mx(t) be its moment-generating function. Define Rx(t) = In(Mx(t)). (a) Show that Rx(0) = 0. (b) Show that R'x(0) = E(X). (c) Show that RK (0) = V(X). (d) Suppose that Mx(t) = e5(et–1). Find E(X) and V(X) in two different ways: first by differen- tiating Mx(t), and then by differentiating Rx(t).