Problem 3 DNA Methylation
DNA methylation is a process by which methyl chemical groups are attached to the DNA. Thus
each gene in the genome can be methylated or unmethylated.Suppose that 80% of methylated
genes remain methylated and 50% of unmethylated genes remain unmethylated each generation.
(a) Express methylation model with the recursion x_(t+1)=Ax_(t)
(b) Calculate the eigenvalues of A.
(c) What is the long-term behavior of x_(t)
(d) Using the initial condition x_(0)=[} a 1-a ] , express the solution to the recursion in terms of the
eigenvectors and eigenvalues of A.