1. A nefarious gambler has developed a weighted six-sided die, with sides marked 1,2,3,4,5, and 6. The probability that a 6 is rolled is 0.4, and all the other sides are equally likely. Define the random variable X = the value on the die when it is rolled once.
2. (a) Write out the probability distribution function of X. (b) Compute the probability that an even number is rolled. (c) Compute the expectation and variance of X.