The state of michigan generates a three-digit num-ber at random twice a day, seven days a week for its daily 3 game. the numbers are generated one digit at a time. consider the following set of 50 three-digit numbers as 150 one-digit integers that were generated at random: 169 938 506 757 594 656 444 809 321 545 732 146 713 448 861 612 881 782 209 752 571 701 852 924 766 633 696 023 601 789 137 098 534 826 642 750 827 689 979 000 933 451 945 464 876 866 236 617 418 988

let x denote the outcome when a single digit is generated.

(a). with true random numbers, what is the pmf of x? draw the probability histogram.

(b). for the 150 observations, determine the relative frequencies of 0,1,2,3,4,5,6,7,8, and 9, respectively.

(c). draw the relative frequency histogram of the observations on the same graph paper as that of the probability histogram. use a colored or dashed line for the relative frequency histogram