STATISTC 515 Final: STAT 515 UMass Amherst STAT515Summer2016FinalSoln
Document Summary
In problems that require reasoning, algebraic calculation, or the use of your graphing calculator, it is not su cient just to write the answers. You must explain how you arrived at your answers and show all your algebraic calculations: use any method you prefer for the problems below: (a) suppose that z has a standard normal distribution. Find the density function of the random variable u = z 2. Hints: you may identify the distribution of u using the tables provided. If v is normally distributed with mean 0 and variance 2 (that is v n (0, 2)) , then r (b) let z have a uniform distribution on (0, 1). Show that w = 2 ln(z) has an exponential distribution. Find the moment-generating function for the bernoulli random variable y1. (ii). Find the moment-generating function for w = y1 + y2 + + yn. (iii). Determine the distribution of w by using the result in (ii).
