Posted by **miranda** on Thursday, April 23, 2009 at 4:36pm.

let the random variable x denote the number of girls in a five-child family. if the probability of a female birth is .5

find the probability of 0,1,2,3,4, and 5 girls in a five-child family.

construct the binomial distribution and draw the histogram associated with the experiment

compute the mean and the standard deviation of the random variable x

- math -
**Damon**, Thursday, April 23, 2009 at 5:43pm
for binomial coefficients use

C(n,k) = n!/(k![n-k]!)

here n = 5 and k is zero through five

or just use Pascal triangle

for n = 5

they are:

1 5 10 10 5 1

then

P(k girls) = C(n,k) p^k p^(5-k)

so for example

p(4 girls )= 5 (.5)^4 (.5)^1

= 5 (.5)^5 = .15625

The mean of a binomial distribution = n p so here = 5(.5) = 2.5

The sigma^2 = n p (1-p)

so here sigma^2 = 5(.5)(.5) = 5/4

so sigma = (1/2) sqrt 5 = 1.12

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