To test the hypothesis that parents name their children without bias towards their own initials we have data of one parent name and one of their children's names. There are 600 data points and it has been measured that roughly 7% of parents have names that start with the same first initial as their own.
If there is no such tendency, what is the expected rate of parent-child first initial matches? Is it as simple as 1 in 26 (letters in the alphabet)? What would be the best way to go about it? Could you use distribution of children's names?