Given target row totals {r_i > 0) and column totals {c_j > 0):

a. Explain how to use IPF to adjust sample proportions {p_ij} to have these totals but maintain the sample odds ratios.

b. Show how to find cell proportions that have these totals and for which all local odds ratios equal θ > 0. (Take initial values of 1.0 in all cells in the first row and in the first column. This determines all other initial cell entries such that all local odds ratios equal θ.)

c. Explain how cell proportions are determined by the marginal proportions and the local odds ratios.