Reflecting random walk on the line. Consider the points 1; 2; 3; 4 to be marked on a straight line. Let Xn be a Markov chain that moves to the right with probability 2=3 and to the left with probability 1=3, but subject this time to the rule that if Xn tries to go to the left from 1 or to the right from 4 it stays put. Find (a) the transition probability for the chain, and (b) the limiting amount of time the chain spends at each site

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.

Evaluate 5 + 6 · 2 – 8 ÷ 4 + 7 using the correct order of operations. a. 22 b. 11 c. 27 d. 5

Scenario: susan wants to make 2 square flags to sell at a crafts fair. the fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over. what's the least amount of fabric she should buy? question: which equation will susan solve her problem? note: let x represent the length of 1 side of the flag. options: 1) 2x^2 = 4x 2) 8 +2x = 2(4x) 3) 2 * 2 = 4 * 2 4) 4x^2 -2x = 0