What is the best estimate of the probability of a male offspring based on the observed data? 

Demography

A common assumption is that the gender distributions of successive offspring are independent. To test this assumption, birth records were collected from the first 5 births in 51,868 families. For families with exactly 5 children, Table 10.35 shows a frequency distribution of the number of male offspring (from Data Set SEXRAT.DAT; see p. 110).

Table 10.35: Frequency distribution of number of male offspring in families of size 5

Number of male offspring _________________ n

0 ……………………………………………….. 518

1 …..………………………………………….. 2245

2 ………………………………………………. 4621

3 ………………………………………………. 4753

4 ………………………………………………. 2476

5 ………………………………………………. 549

Total ……………………………………..… 15,162

Suppose the investigators doubt the probability of a male birth is exactly 50% but are willing to assume the gender distributions of successive offspring are independent.