Currently very confused about lecture problems, please explain thoroughly in R programming.

Problem 1: In the US population the average adult male popu- lation is normally distributed with a mean of 69 inches and with a standard deviation of 2.9 inches. For the adult female population the distribution is with a mean of 64 inches and with a standard deviation of 2.7 inches. (i) Suppose a random male and a random female are chosen from the population determine the probability that the female will be taller than the male. Solve this problem mathematically. (Hint: The inequality F > M and be rewritten as F - M > 0. Now use the well-familiar fact that a linear combination of inde- pendent normals is normal.) (ii) Solve this problem by running a simulation. Draw indepen dent samples from the two normal distributions and find how fre- quently the female population exceeds the male population. Com- pare your two answers. Problem 2: Suppose X is a two-dimensional random variable whose two-dimensional PDF is given by, fx(s, t) xx (1 - st) supported on (0, 1) x (0, 1) (i) Calculate the probability that, P(X