When two births are randomly selected, the sample space for genders is bb, bg, g

Question

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? For the entire population, assume the probability of having a boy is . the probability of having a gil is z. and this is not affected by how many boys or girls have previously been borm. Determine the probabilities of each sample proportion Sample proportion of girls Probability (Type integers or simplified fractions.)

Explanation / Answer

from given data: P(X=0)=P(X=0 girls out of 2)=P(both are boys)=(1/2)*(1/2)=1/4

hence

sample proportion probability 0           1/4    1/2    1/2 1           1/4

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