Below is a table giving a joint pmf for the random pair (y,x).
|
x=1 |
x=2 |
x=3 |
|
y=3
|
.05 |
.2 |
.1
|
| y=2 |
.1 |
.1 |
.11 |
| y=1 |
.15 |
.1 |
.09 |
a) Find the SEL predictor of y based on x. (You need to evaluate all of y opt(1), y opt(2), and y opt(3)) Evaluate the risk of this predictor.
b) Find the 0-1 loss predictor of y based on x. (Again need to evaluate all of y opt(1), y opt(2), and y opt(3)) Evaluate the risk of this predictor.