Atotal of m white and m black balls are distributed among two urns, with each urn containing m balls. at each stage, a ball is randomly selected from each urn and the two selected balls are interchanged. let xn denote the number of black balls in urn 1 after the nth interchange.

(a) give the transition probabilities of the markov chain xn, n 0.
(b) without any computations, what do you think are the limiting probabilities of this chain?
(c) find the limiting probabilities and show that the stationary chain is time reversible.

The weight of 46 new patients of a clinic from the year 2018 are recorded and listed below. construct a frequency distribution, using 7 classes. then, draw a histogram, a frequency polygon, and an ogive for the data, using the relative information from the frequency table for each of the graphs. describe the shape of the histogram. data set: 130 192 145 97 100 122 210 132 107 95 210 128 193 208 118 196 130 178 187 240 90 126 98 194 115 212 110 225 187 133 220 218 110 104 201 120 183 124 261 270 108 160 203 210 191 180 1) complete the frequency distribution table below (add as many rows as needed): - class limits - class boundaries - midpoint - frequency - cumulative frequency 2) histogram 3) frequency polygon 4) ogive