When two births are randomly selected the sample space for g

When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?

Determine the probabilities of each sample proportion.

Solution

The number of girls possible are 0,1,2. Now probability of no girl is 0.25, probability of 1girl is 0.5 and probability of 2girls is 0.25 using the four outcomes.

The mean of the number of girls is = 0*0.25+1*0.5+2*0.25=1

The mean of the sample proportion is equal to the population proportion