I've been given a Markov chain problem for homework. The unfortunate part is that we will not have time to cover this material in class. So, it is learn it yourself!
Here is the initial data:
"Consider a variety of rose that can have either a pale hue or a brilliant hue. It is known that seeds from a pale blossom yield plants of which 60% have pale flowers and 40% have brilliant flowers. Seeds from a brilliant blossom yield plants of which 30% have pale and 70% have brilliant flowers."
This is what I am stuck on:
"Now, let p and b represent the proportion of plants with pale and brilliant hues, respectively, and suppose the proportions do stabilize. Then, the proportion of flowers in the next generation that are pale is .6p + .3b. (Why?) But since the population has stabilized, the proportion of pale flowers in the next generation must remain the same as it was. Write an equation to represent this situation:
Similarly, the proportion of flowers that are brilliant in the next generation after the population has stabilized will remain the same. Write an equation to represent the situation for the brilliant flowers."
If anyone can help me understand this, I would greatly appreciate it! It is due on Tuesday evening, and I've been working on this for over a week trying to figure it out myself. Thank you!