OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 28J / b / iv / Solution

The Markov property and conditioning on the intermediate state give the bridge probability

P (X_{t} = 2 ∣ X_{0} = 1, X_{3 t} = 1) = \frac{p _{12} ( t ) p _{21} ( 2 t )}{p _{11} ( 3 t )} .

Substitution from part (i) yields

\frac{λ μ ( 1 - e ^{- s t} ) ( 1 - e ^{- 2 s t} )}{s ( λ + μ e ^{- 3 s t} )} (s = λ + μ) .

Solved by gpt-5.6-sol high.

 Ancestors (12)