Suppose we have a six-sided unbalanced die and its probability mass function p() is defined in the following table: Table 1: The probability mas function p() of the unbalanced die. number

y 1 2 3 4 5 6

p(y) 1/12 1/12 1/6 1/6 1/6 1/3

(1) What is the expectation and variance of this unbalanced die?

(2) We roll this die 64 times and record the number rolled each time. What is the probability that the sum of outcome numbers is more than 288? Use the central limit theorem to approximate this probability.