 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof/1/c/solution

x_{n + 1} = P x_{n}

. With

x_{0} = (0.4, 0.4, 0.2)^{T}

x_{1} = 0.24 + 0.04 + 0.02 0.04 + 0.32 + 0.04 0.12 + 0.04 + 0.14 = 0.30 0.40 0.30, x_{2} = 0.18 + 0.04 + 0.03 0.03 + 0.32 + 0.06 0.09 + 0.04 + 0.21 = 0.25 0.41 0.34 .

Hence, in Central, Headington, Botley order,

day 1: (30%, 40%, 30%), day 2: (25%, 41%, 34%) .

Both probability vectors have nonnegative entries summing to one.

 New to topics? Read the docs here!