A die has 5 sides, not 6 like a regular die. The five sides are labeled 1, 2, 4, 8, and 16 respectively. It is equally likely that you will get a 1 or an 8. It is equally likely that you will get a 2 or a 4. It is two times more likely that you will get a 16 than an 8. It is four times more likely that you will get a 4 than a 1.

1. Let X = the outcomes of a roll of the die. Find the probability mass function of X.
2. If Y=2X2+1, find PY(y). Hint: if the outcome of RV X is 1, then the outcome of Y is 2*12+1=3, if the outcome of RV X is 2, then the outcome of Y is 2*22+1=9.
3. If I roll the die ten times, what is the probability that I get exactly 4 twos?