A Poisson random variable has a PMF of the form
k = 0,1,2.....
(a) Find the characteristic function ![](https://test.transtutors.com/qimg/a6069bfa-e7bc-471d-8d31-769cea68e8b9.png)
(b) Find the first three nonzero terms in the Taylor series expansion of ![](https://test.transtutors.com/qimg/d8cf20a5-38e8-47cd-a6fc-769bae1f6749.png)
(c) Use the results of part (b) to find the mean, variance, and skewness of the Poisson random variable.