You toss a fair tetrahedral (4-sided, and the sides are marked "1", "2", "3", and "4") die, and you play the following game repeatedly. For each game, you throw the die n > 3 times. Starting from the third throw of the current game, right after each throw, you will get 1 dollar if the total number of points on the last three throws is 8 or higher, and you pay 1 dollar otherwise. It is possible to verify that your probability of winning one dollar on the third throw is 0.5. The random variable Xi represents the outcome of the i th throw. Required:
Find the expected value of your total gains/losses over one game in terms of n.

(c) compare the results of parts (a) and (b). in general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c. there is no distinct pattern when each data value is multiplied by the same constant. (d) suppose you have information about average heights of a random sample of airline passengers. the mode is 65 inches, the median is 72 inches, and the mean is 65 inches. to convert the data into centimeters, multiply each data value by 2.54. what are the values of the mode, median, and mean in centimeters? (enter your answers to two decimal places.) mode cm median cm mean cm in this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. consider the following data set 7, 7, 8, 11, 15. (a) compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = (b) multiply 3 to each of the data values. compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = --