We consider the experiment of rolling two different fair dice (at the same time), and let X be a random variable representing the difference between the two numbers that appear. Then:
a) Determine the probability mass function P(X).
b) Determine the distribution function F.
c) Calculate the mean and variance of X.
d) Sketch the functions in parts (c and d).
7) Let X be a discrete random variable with probability mass function P(X = k) = c, where k = 1, 2, 3, 4, 5, 6.
a) Determine the value of the constant that makes it a probability mass function.
b) Calculate E(X^2) and var(5X - 1).