This one's easy, I'll take a crack.

Firstly, the odds:

JJ vs any underpair = 80%
JJ vs any overpair = 20%
JJ vs itself = 50%
JJ vs AQ or AK = 56% <font color="red">**</font>

Now we have to work out the frequency at which each of our opponent's holdings occur. These are the holdings we're interested in:

Lower pocket pair: 22,33,44,55,66,77,88,99,TT = 9 lower PP
Higher pocket pair: QQ,KK,AA = 3 higher PP
JJ = 1
AK, AQ = 2

We're almost there, we just need to work out the frequency of those holdings. In a random deal there are:
-6 of any pocket pair possible (because of suits)
-16 of any two unpaired cards (AK, AQ) possible

So we have:

Lower PP: 9*6 = 54 total possiblities
Higher PP:3*6 = 18 total
AK,AQ: 2*16 = 32 possible
JJ = 1 possible

So, our EV against this range is the sum of:
(frequency of each hand occuring)*(probability of JJ winning against that hand) / the total number of hands

= [(54*0.8) + (18*0.2) + (32*0.56) + (1*0.5)]/105 = 65.22/105 = 62.11%

Therefore, JJ against his hand range is 62% favored to win.
I'd just caution this hand range is probably only applicable late in a tournament against certain opponents.


**Note that I have included the weighted average of suited and offsuit AK and AQ, so the numbers are correct.