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

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?
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Demi-Leigh Barrera
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:
$\mu =\sum P\left(X\right)=0\ast 0.625+1\ast 0.25+2\ast 0.375+3\ast 0.25+4\ast 0.0625=2$
The standard deviation is the square root of the sum of the squared deviations multiplied by the probability:
$\sigma =\sqrt{\sigma \left(x-\mu {\right)}^{2}P\left(X\right)}=\sqrt{\left(0-2{\right)}^{2}\ast 0.0625+...+\left(4-2{\right)}^{2}\ast 0.0625}=2$
It is unusual to get 4 girls, because 4 is standard deviations from the mean.
Result: