Suppose we have two dice, one of which is standard (has faces with the numbers 1, 2, . . . , 6) and another which is special (has the number 0 written on three of the faces and 6 written on the other three). Now suppose we throw the two dice and let X denote the random variable that is the sum of the values on the observed faces.(a) What is the range of X? (give exact upper and lower bounds along with a line of explanation)(b) What is the probability mass function of X?(c) What is the cumulative density function of X?

Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. kevin spins the spinner 180 times. kevin determines about how many times the spinner will land on red or green, and his work is shown below. -kevin has the formula reversed; it should be the total number of sections over the number of red or green sections. -kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections. -kevin should multiply by the number of sections in the spinner rather than the total number of spins. -kevin calculated the prediction correctly and did not make any mistakes.