1.31 Refer to Section 1.5.6. Let a denote the number of calves that got a primary, sec-

ondary, and tertiary infection, b the number that received a primary and secondary but not a tertiary infection, c the number that received a primary but not a secondary infection, and d the number that did not receive a primary infection. Let π be the probability of a primary infection. Consider the hypothesis that the probability of infection at time t, given infection at times 1,..., t - 1, is also π, for t = 2, 3. Show that t = (3a + 2b + c)/(3a + 3b + 2c + d).