E) Present the probability distribution for the sum of two six-sided dice (i.e., list the possible values of the random variable, X and each value's corresponding probability) in your document. Use the x-axis above and rules of theoretical probability to help you calculate your probabilities. (Hint: there are 36 outcomes.) Present the probabilities as fractions (simplified or not simplified) or decimals (rounded to four decimal places) in a table. Note: You will use this table to calculate your theoretical probabilities in parts (f), (g), and (h).

f) Now calculate the theoretical probability that the player lands on "Reading Railroad" on their first turn. Using the probability distribution built in part (e), state this probability as a decimal rounded to four decimal places in a sentence.

g) Calculate the theoretical probability that the player will move no farther than "Reading Railroad" on the first turn. Using the probability distribution built in part (e), state this probability as a decimal rounded to four decimal places in a sentence.

h) Calculate the theoretical probability that the player moves farther than "Reading Railroad" on their first turn. Using the probability distribution built in part (e) state this probability as a decimal rounded to four decimal places in a sentence.

i) Compare your empirical probabilities found in the simulations in parts (b)-(d) to the theoretical probabilities found using the probability distribution in parts (f)-(h) using one sentence for each comparison. Remember to include the values in your comparisons and use the context of the question in your answer. Please reference the assignment instructions on page 1 for an explanation of comparative language.

j) What space would a Monopoly player be most likely to land on for their first turn? Write your answer in a complete sentence with a valid reason.

grAPH D

Rolling 2 dice with 6 sides Event Count Total Proportion Sum of 2 rolls = 5 114 1000 0. 114 Frequency 150 100 50+ 12 Sum of 2 rollsRolling 2 dice with 6 sides Event Count Total Proportion Sum of 2 rolls > 5 733 1000 0.733 Frequency 150 100 50+ 8 10 12 Sum of 2 rolls