Question #335897

If x represents the number of voys in a family of 7 children, find the probabbility and distribution

1
Expert's answer
2022-05-03T16:24:05-0400

XBin(n,p)X\sim Bin(n, p)

n=7,p=q=0.5.n=7, p=q=0.5.


P(X=k)=(7k)(0.5)k(0.5)7k=(7k)128P(X=k)=\dbinom{7}{k}(0.5)^k(0.5)^{7-k}=\dfrac{\dbinom{7}{k}}{128}


xp(x)01/12817/128221/128335/128435/128521/12867/12871/128\def\arraystretch{1.5} \begin{array}{c:c:c} x & p(x)\\ \hline 0 & 1/128\\ \hdashline 1 & 7/128\\ \hdashline 2 & 21/128\\ \hdashline 3 & 35/128\\ \hdashline 4 & 35/128\\ \hdashline 5 & 21/128\\ \hdashline 6 & 7/128\\ \hdashline 7 & 1/128\\ \hdashline \end{array}



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