After years' study in probability, I felt more and more happy with the construction of probability space, it's so simple seemingly but interesting that may be applied to many more areas rather than math.

Let’s review a little bit about the probability space in math. Given a space (\Omega, \mathbb{F}, \mathbb{P}), assume that there exists a r.v X s.t. \{\omega|X(\omega)>0\}\in\mathbb{F}, then we can measure the events \{X>0\} by using \mathbb{P}(X>0). What’s more, adding a time dimension to make it a stochastic process X_t(\omega), then we have properties like \mathbb{F}_t\subset\mathbb{F}_{t^+} and so on.

Secondly, let’s consider another fact, different people have different decisions when given tasks, why is that? That apparently depends on the knowledge we own, how do I relate this decision making base on probability space construction idea? This attracts me these days and I’ll post what I think later.

To be continued……


Trip to Mount Emei

During this summer vacation back in home, I visited Mount Emei in Chengdu, Sichuan with my cousin. It was quite
a tough but pleasant trip in my view. It was tough because among a couple ways to get to the top, we walked the longest and the most difficult one within almost one day, pleasant because of the satisfaction finally compared with the other hikers who thought impossible to achieve it in one day.

Unlike the hikings in the states, hiking the Mount Emei is almost climbing the stairs all the way, sometimes steep enough and sometimes gradual. We started our trip on July 24th afternoon from the foot of the mounting, Baoguosi. According to our plan, we will be staying around Guangfusi, at about 1/6 location of the whole route, so the first day hiking is really just a warm-up exercise, though we still almost couldn’t get to the scheduled staying place before the dark.

On July 25th morning, we started out at 9:00 am, the first destination was Monkey area, those monkeys were more naughty than any child, as long as they saw travellers’ food or bottled water exposed outside backpack, they would grab them away without any doubt. At beginning, my cousin and I were both excited about the monkeys, later in the trip whenever we came across several ones on the road, we were both cautious in case they would grab our food.

If someone asks what the most difficult part of the hiking was, it would definintely be “Ninty nine turnings”, right after the monkey area, it was the steepest and longest continous stairs with 15km length if I was right. We spent hours dealing with this period, the situation was like, we had to take a one minute rest after every one minute’s walk! One funny thing is that, even in such a narrow and difficult way, you can ask someone to carry you up to the top of the Mounting, by sitting on a sedan chair carried by two people. The price is around ¥1500 per trip, usually, those businessman from Hongkong or Guangzhou would asks such a helper as we met at the day there.

As I remember, the distance between Hongchunpin and Jinding(the mounting top) was 42km, we met so many travellers on the way, those who sit in sedan chair carried by others, those pilgrims who also head to Jinding, but only us, planned to walk to the top at the day. We also felt afraid sometime during the trip, but we made it finally, get to Jinding at 10:00pm, after more than 12 hours climbing.