A STEM degree is one involving study in science, technology, engineering and mathematics and refers to any subjects that fall under these four disciplines.

X/Y	Non Stem Y =0	Stem =1
Unemployed X=0	0.05	0.01
Employed X=1	0.72	0.22

Part A 1. Find the marginal distributions of X and Y. 2. Determine the unemployment rate in Canada and show that this is also given by [1- E(X))]. Note: the unemployment rate is the percentage of the labour force that is unemployed. 3. What is the probability that a person in this population is (i) a STEM worker and unemployed (ii) a STEM worker given that she is unemployed, and (iii) an employed worker. 4. Determine both conditional distributions of Y. 5. Are type of degree and labour force status independent? Explain.

B. Suppose a random variable Y has a normal distribution with means a and variancle b2. Derive the mean and variance of [(Y/b) -(a/b)].