Problem 5: Suppose that X is a random variable for which the moment generating function (m.g.f.) is as follows: ψ_X(t) = {6}/{1} (4 + eᵗ + e⁻²ᵗ) . Find the probability distribution of X .
Hint: It is a simple discrete distribution, for example, P(X=0) = 0.3 , P(X=1) = 0.7 .