ities are defined by the first row of <span class="math inline">\(P\)</span>. Our chain can either remain in state <span class="math inline">\(1\)</span> with probability <span class="math inline">\(P_{11}\)</span> or transition to state <span class="math inline">\(2\)</span> with probability <span class="math inline">\(P_{12}\)</span>. Therefore, to simulate <span class="math inline">\(X_1\)</span>, we must generate a random variable according to the probabilities <span class="math inline">\(P_{11}= P(X_1 