For two data points X1, 22 that can each take on a value in 1, 2, ...,30, let's define a function f2(k) to represent the number of arrangements in which x1 + 22 takes value k. We've shown that for k outside of the range [2, 60], we have f2(k) = 0. We've also established that f2(2) = 1 and f2(60) = 1.d) 6060 What if we look at 3 data points, instead of 2? In that case, we are looking at the distribution of (x1 + 2 + 23)/3, where x1 + x2 + 23 takes a value from 3, 4, ..., 89, 90. Define a function f3(k) to represent the number of arrangements in which x1 + x2 + 3 takes value k. Express f3(k) in terms of f2(k). Your expression should contain a summation symbol _, and there is no need to expand and simplify it. e) For an arbitrary n, define a function fn (k) to represent the number of arrangements in which n xi takes value k. i=1 Express fn+1 (k) in terms of fn(k). Your expression should contain a summation symbol _, and there is no need to expand and simplify it. n f ) From the above question, we have the number of arrangements for which the total xi takes i=1 n value k. What is the probability Pn (k) that E xi takes on value k? i= 1