2 students from STAT 401 are selected at random and their opinions about the use of clean energy are recorded on a scale from 1 to 3. In other words, an outcome of this experiment takes the form (S1, S2), where S1 is the opinion of student 1, and can take a value from 1 to 3. Answer the following questions and show all relevant work.

1.) How many outcomes are there in the sample space of the above experiment?

2.) In another experiment, instead of recording the opinions (S1, S2), we record only the sum of 2 opinions. In other word, an outcome of this new experiment is a single number T = S1 + S2. How many outcomes are there in the sample space of the above experiment?

3.) Assume equally likely outcomes. Give the pmf of the random variable T = S1 + S2 in part 2 in tabular form. (Tabular form means the same table in example 2.3-13).

Give answers indecimalform,round to 2 decimal places. For example, instead of 1/3, use 0.33