. The nucleotide diversity Πn among a set of n aligned sequences was introduced in Section 13.8.2. It is defined by where dij is the number of segregating sites between sequences i and j. (This is the...

.
The nucleotide diversity Πn among a set of n aligned sequences

was introduced in Section 13.8.2. It is defined by

where dij is the number of segregating sites between sequences i and j. (This is

the Hamming distance between the sequences.) Show that under the infinitely

many sites model of mutation, the expected value of the nucleotide diversity

is θ.

.
In Section 13.8.3 we found a formula for ETMRCA for a sample of

n genes. Calculate the variance of TMRCA and find its value for large samples.