Consider the experiement of rolling two identical fair 4side

Consider the experiement of rolling two identical fair 4-sided dice. The sample space S of this experiment consists of 16 ordered pairs of numbers, all equally likely. (If it helps, imagine that one die is red and the other is green.) Define a random variable X to be the different (i.e. subtraction) between the larger and small face values on a single roll of the two dice.

2. Give the probablity mass function (pmf) for X. Use fractions or decimals to 4 places.

3. For the next parts use your answer in part (2).

4. Determine the expected value E(X) of X.

5. Determine the vairance and standard deviation of X.

6. Give the cumulative distribution function (cdf) of the rv Y, based on your table in part (2), and sketch its graph on the axis.

Solution