When you say that y coordinate is even or odd you mean on what number the entire hex ends?
Yes, but not the hex you have quoted.
The hex you have quoted -
02f9fd63b1121b8872d6184b39e97972cd636e76a0fa9c67a74b1b7156791f1381 - is the compressed public key. It is the initial
02 byte followed by the x coordinate only. The y coordinate has been omitted because it can be calculated from knowledge of the x coordinate and the initial byte. The full uncompressed key is:
04f9fd63b1121b8872d6184b39e97972cd636e76a0fa9c67a74b1b7156791f138195d1c7407dee48a9b4796494c1c23824e90614b7a84aea43242922a48699bd8e
This is made up of the following
Initial byte - 04 (which tells us the key is uncompressed)
x coordinate - f9fd63b1121b8872d6184b39e97972cd636e76a0fa9c67a74b1b7156791f1381
y coordinate - 95d1c7407dee48a9b4796494c1c23824e90614b7a84aea43242922a48699bd8e
So to compress this, you drop the y coordinate, and since the y coordinate is even, turn in the initial
04 byte to
02.