Random variable

[KarterWhite]

Guys, I got this task that I couldn't solve. I will be very grateful for the detailed explanation.

Random variable x represents 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?

I will be incredibly grateful for your help with the decision.

 

[Buckeye]

I would say step one is to list the possible outcomes for 4 children. Do you know how to do that?

 

[AngleWyrm]

Random variable x represents the number of girls in a family of four children.

Binomial Distribution

Mean μ = np
Variance σ2 = npq
Standard Deviation σ= √(npq)

 

[Zaid Gray]

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
You can go to the page https://plainmath.net/2801/variable-represent-children-construct-describing-probability-distribution where you will find a more detailed explanation of the solution of this problem.