(10 points) let x be a random variable with moment generating function mxptq "" 1 3 e 8t ` 1 6 e ´2t ` 1 3 e ´8t ` 1 6 e 2t . a) use the derivatives of mxptq to find the mean and variance of x. b) find the probability mass function of x and use it to check your results for the mean and variance you derived in a).
