Proper Divisors Problem: An integer from 1 through 10 is selected at random. Let x be

Chapter 9, Problem 11

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Proper Divisors Problem: An integer from 1 through 10 is selected at random. Let x be the number of proper divisors the integer has. (A proper divisor of an integer n is an integer less than n that divides n exactly. For example, 12 has five proper divisors: 1, 2, 3, 4, and 6.) a. List the proper divisors and the number of proper divisors for each integer from 1 through 10. b. For each possible value of x, identify how many of the integers from 1 through 10 have that number of proper divisors. c. Let P(x) be the probability that an integer from 1 through 10 has x proper divisors. Calculate P(x) for each value of x in the domain. d. Plot the graph of the probability distribution in part c. Do you see any pattern followed by the points on the graph?