I am using a textbook titled Elementary Statistics by: MarioF. Triola. there is

Question

I am using a textbook titled Elementary Statistics by: MarioF. Triola. there is a homework question I don't quiteunderstand. How do I even start? The question is: Let the random variable x represent thenumber of girls in a family of four children. Construct a tabledescribing the probability distribution, then find the mean andstandard deviation. Is it unusual for a family of four children toconsist of four girls? I am using a textbook titled Elementary Statistics by: MarioF. Triola. there is a homework question I don't quiteunderstand. How do I even start? The question is: Let the random variable x represent thenumber of girls in a family of four children. Construct a tabledescribing the probability distribution, then find the mean andstandard deviation. Is it unusual for a family of four children toconsist of four girls?

Explanation / Answer

here are the possibilities: BBBB (0 girls: only 1 way) GBBB BGBB BBGB BBBG (1 girl: 4ways) GGBB GBGB GBBG BGGB BGBG BBGG (2 girls: 6 ways) GGGB GGBG GBGG BGGG (3 girls: 4 way) GGGG (4 girls: 1 way) There are 16 possible outcomes. P(X=0) = 1/16 P(X=1) = 4/16 = 1/4 P(X=2) = 6/16 = 3/8 P(X=3) = 4/16 = 1/4 P(X=4) = 1/16 mean = (1/16)*0 +(4/16)*1+(6/16)*2+(4/16)*3+(1/16)*4 = 32/16 =2 variance =(1/16)*(0-2)2+(4/16)*(1-2)2+(6/16)*(2-2)2+(4/16)*(3-2)2+(1/16)*(4-2)2= 16/16 = 1 SD = (1) = 1

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