Suppose that T n has a Poisson distribution with mean = n, for fixed > 0. For large n, show that the distribution

Suppose that T_n has a Poisson distribution with mean λ = nµ, for fixed µ > 0. For large n, show that the distribution of log T_n is approximately normal with mean log(λ) and variance λ^–1. [By the central limit theorem, T_n/n is approximately N(µ, µ/n) for large n.]