Find a continuous-time birth and death model on the state space {1, 2, 3, … } that has

3. Find a continuous time birth and death model on the state space {1, 2, 3, … } that has stationary distribution
6 7r(x) = 7r x2. To be clear: you must provide the rates up, q(x, x + 1) = Ax, and down q(x, x — 1) = fix for each x E {1, 2, 3, … }. Also, I care more about how you find your solution than whether or not you get it correct. Therefore, most points will be given based upon your methodology, and I want you to show me how you came up with your solution. Simply providing rates and no explanation will result in zero points.