# Question: The state of Michigan generates a three digit number at random

The state of Michigan generates a three-digit number 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:

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.

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.

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