Let S be the sample space when a fair 6-sided die is rolled twice. Define a random variable X as follows: X=x-y], x= outcome from the 1st roll, y = outcome from the second roll. Then X is a random variable of discrete type. a. Find S, the support or space of X. b. Determine f(x), the pmf of X. c. Show that f(x) = 1 for the pmf. 145, d. Define A={xeSx,x is odd number}. Find P(4). e. Graph the pmf of X as a line graph. 2. For each of the following function below, determine the constant c so that f(x) satisfies the conditions of being a pmf for a random variable X- (1) f(x)=x=1,2,3.4. (ii) f(x) =cx, x=1,2,....9,10. (iii) f(x) = c(x+1), x=0,1,2,3. . For each pmf above, determine F(x), cdf of X. 3. Let a random experiment be the casting of the pair of fair six-sided dice and be the minimum of the two outcomes. a. With reasonable assumptions, find f(y), the pmf of Y b. Draw a probability histogram of f(y).