That's spot on. It is exactly 12.75 (and stdDev = 3.326...).
my computation indicates that

mean(n) = n/8 + 1/4 for n > 1

Can not find fault in your reasoning: (50+0)/2 = 25 and it works for n=2;
althought n=100 and we are looking for a mean not an average.

What's the expected number of 1-runs when tossing a fair coin 100 times;
where 1-run (for heads) is defined as HT or H for the last toss;
for example: THHTHTHTTH has 3 1-runs.

what's the distribution of (X1,X2)?

Thanks Martinghoul, I am wondering what's the ASW liquidity for bunds (and other German gov bonds) vs bonds liquidity.

What's the market practice regarding collateral posting for asset swaps. I would think that mark to market of (Libor+spread - coupon payments) is computed and corresponding collateral is posted i.e. bond price is not relevant.