The probability that a computer running a certain operating system crashes on a given day is 0.1. Let X be the random variable equals to the number of operating days before crash occurs the first time. (a) Write down the probability mass function of X. [3] (b) Find the probability that the first crash occurs on the twelfth day. [1] (c) Find the probability that the first crash occurs by the fourth day. [2] (d) What is the expected number of days before computer crashes? [1] 5