2.1 Marginal and conditional probability: The social mobility data from Sec- tion 2.5 gives a joint probability distribution on (Y1, Y2)= (father's oc- cupation, son's occupation). Using this joint distribution, calculate the following distributions: a) the marginal probability distribution of a father's occupation; b) the marginal probability distribution of a son's occupation; c) the conditional distribution of a son's occupation, given that the father is a farmer; d) the conditional distribution of a father's occupation, given that the son is a farmer. son's occupation father's occupation farm operatives craftsmen sales professional farm operatives 0.018 0.035 0.031 0.008 0.018 craftsmen sales professional 0.002 0.112 0.001 0.066 0.001 0.018 0.001 0.029 0.064 0.032 0.069 0.094 0.032 0.084 0.019 0.010 0.051 0.032 0.043 0.130