A random experiment is to roll a dice. The corresponding random variable X is defined 

as follows. X = i when a number i appears. i can be 1,2,3,4,5,6. The dice is fair. (a) Draw probability mass function. (b) Draw distribution function(i.e., Cumulative distribution function) (e) What is the expectation of X? 2. A random variable y follows a uniform distribution on [0, 1], It means that the random variable Y takes any value between 0 to 1. (a) What is the probability density function of Y, fy (y)? (b) What is the distribution function of T, Fy(y) = Pr[Y y]? (e) What is the expectation of Y? (d) What is the 40 percentile of Y? 3. Suppose that there are two discrete random variables, W and Z Table 1: A joint probability of W and Z Z=0 Z=1 W = 0 1/12 1/6 W = 1 2/3 1/12 (a) What is the marginal probability of W?(that is, compute Pr[W= w] for all w = 0, 1.)