Define yt x1 t x2t at any time t argue that yt t ge 0 is

Question

Let {X₁ (t), t ≥ 0} and {X₂ (t), t ≥ 0} be independent two-state continuous-time Markov Chains on the state's 0 and 1 having the same generator matrix

Define Y(t) = X₁ (t) + X₂(t) at any time t.

Argue that {Y(t), t ≥ 0} is a continuous-time Markov Chain on the states {0, 1, 2} and determine its generator matrix.