Analyze and answer the problem. Two fair dice are thrown; one is red and the other is blue. Let D represent the outcome of the red die minus the outcome of the blue die. Write all answers in a whole sheet of graphing paper. Show all necessary solutions. I. Give the sample space and the range space. II. Construct the probability mass function and the corresponding histogram for the random variable D. III. What is the mean of the distribution? Interpret the result. IV. Compute the variance and standard deviation. Interpret the results.