Disliked{image} Now in the picture above, on any branch of the tree you move up/down depending on whether the next value is higher/lower. Apart from the two fails, all branches give you one of those conditions. therefore, if we stop here, we should have probability 14/16=87.5%. But if we look at the two fails, notice that in the top one x(1)<x(3) but x(5) can be lower or higher than x(3). The reverse is the case for the branch below. If x(5) is higher than x(3), we have to split the remaining probability into two. Now, 1-87.5%=12.5%. So, we are interested...Ignored

Disliked{image} Now in the picture above, on any branch of the tree you move up/down depending on whether the next value is higher/lower. Apart from the two fails, all branches give you one of those conditions. therefore, if we stop here, we should have probability 14/16=87.5%. But if we look at the two fails, notice that in the top one x(1)<x(3) but x(5) can be lower or higher than x(3). The reverse is the case for the branch below. If x(5) is higher than x(3), we have to split the remaining probability into two. Now, 1-87.5%=12.5%. So, we are interested...Ignored

here we consider there is X0 for which we mark X1 either up or down

I'm not a programmer and i don't like ! , but only I try to catch my view !