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.