Let X be a random variable with mean and variance 2, and let 1(t) denote the m.g.f. of X for < t <

Let X be a random variable with mean μ and variance σ2, and let ψ1(t) denote the m.g.f. of X for −∞ < t < ∞. Let c be a given positive constant, and let Y be a random variable for which the m.g.f. is ψ2(t) = ec[ψ1(t)−1] for −∞ < t < ∞.
Find expressions for the mean and the variance of Y in terms of the mean and the variance of X.