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. Express 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 the printout of your R workspace.