Assume the probability that a newborn is a boy is 51%, that is, p = 0.51. Suppose a family has 8 children.

a) What is the distribution law followed by the number of boys in such a family?

b) Denote F the cumulative distribution function of this distribution law. Epress each of the following probabilities through the values of F:

i) there are at least 4 boys,

ii) there are at least 4 girls,

iii) all children are boys,

iv) there are exactly 5 boys and 3 girls,

v) there are between 3 and 5 boys.

c) Using R, calculate all of the above values.

Attach a printout of your R workspace.