Suppose the number of daughters of a woman is 0, 1, 2, or 3 with respective probabilities 0.3, 0.4, 0.2, 0.1. Suppose further that the number of daughters of each of her descendants has the same probability mass function and that these variables are independent. Let Xn be the number of daughters in generation n, starting with X0 = 1.
Write out the first three rows of the transition matrix of the Markov Chain whose states are the number of daughters in a generation.
How would I go about doing this?
the other parts to the question were
Find the expected number of daughters in generation 3. Which I found to be 1.33
Find the var(X2), which I found to be 2.0559
Find the probability that in some future generation there are zero daughters, which I found to be .7913
Any help on constructing the markov chain will be greatly appreciated.