Ultrastrators civilization

Question

I came across this question: In the ultrastrators civilization on planet Anachronista, the population is divided into four strata which, in order of status , are labeled Alpha, Betta, Gamma and Delta. By the traditions of the civilization, no child can have a status more than one different from its parents. As examples, in each generation 20% of the children of Alphas grow up to be Bettas, the rest remaining Alphas, while of the Betts offspring 50% remain Bettas while 10% become Alphas and the rest Gammas.

I am asked to find the transitional matrix, per my understanding, the transitional matrix will be a four by four matrix since the population is divided into four strata. I am able to compute the first row [0.8, 0.2, 0, 0] and the second row [ 0.1, 0.5, 0.4, 0]. How will I find the remaining two rows to complete the transitional matrix?

Answer 1

You do not have sufficient information to uniquely determine the transition probability yet.

The following information are still needed:

• Percentage of Gammas that will remain Gammas, percentage of Gammas that will become Betas.
• Percentage of Deltas that will remain Deltas.