Random variable x represent the number of girls in a family of four children. 1) Construct a table describing the probability distribution, then find

Question

Random variable x represent the number of girls in a family of four children.
1) Construct a table describing the probability distribution, then find the mean and standard deviation. (Hint: List the different possible outcomes.)
2) Is it unusual for a family of four children to consist of four girls?

Answer 1

1) The possibilities are (B=Boy and G=Girl): BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGB, GGBG, GGGB, GGGG Every outcome has an equal chance. Let X be the number of girls:
X - Probability
0 - 0.0625
1 - 0.25
2 - 0.375
3 - 0.25
4 - 0.0625
2) The meanis the sum of the product x and the probabilities of x:

μ = \sum P (X) = 0 * 0.625 + 1 * 0.25 + 2 * 0.375 + 3 * 0.25 + 4 * 0.0625 = 2

The standard deviation is the square root of the sum of the squared deviations multiplied by the probability:

σ = \sqrt{σ (x - μ)^{2} P (X)} = \sqrt{(0 - 2)^{2} * 0.0625 + . . . + (4 - 2)^{2} * 0.0625} = 2

It is unusual to get 4 girls, because 4 is standard deviations from the mean.
Result:

μ = 2, σ = 1, U n u s u a l

Random variable x represent the number of girls in a family of four children. 1) Construct a table describing the probability distribution, then find

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