Topic: Independence between random variables

1. To show that two discrete random variables are independent, I only need to show that joint pmf for a pair of values (1,2 ) can be factored into a product of(1) and (2).(True/False)
2. When two discrete random variables are independent, the joint pmf would equal the product of the marginal pmfs for any pair of values these two random variables take. (True/False)
3. Expectation of 1+2 can be computed as the sum of the expectation of the two random variables.(True/False)
4. When two random variables are independent, the expectation of their sum would always be zero.(True/False)