I got some problems with this homework which I have totally no idea, never got into this field before and I really need some help.

First, we have a wiener process like

 [![enter image description here][1]][1]

Which means the probability of the process drops beneath -3 within the time interval [0,1].

Now the thing is **we have to simulate the process by discretize it.**

**1.Suppose we first discretize the process by 100 points and simulate 10,000 process in this way.** 

i.e., W(0.01), W(0.02), …., W(1.00). 

Note that W(t) – W(t-0.01) ~ N(0,0.01) independently. 


**2.Using the data obtained at 1., we approximate**

 [![enter image description here][2]][2] 

**by** 

[![enter image description here][3]][3]

**what is the relationship between this value and the real** 

 [![enter image description here][2]][2] 

**(larger, equal to or smaller)?**

**3.Repeat 1. and 2. by cutting [0,1] into 10,000 points instead. Will the
 resulting probability increases or decreases?**


  [1]: https://i.sstatic.net/7sMvq.png
  [2]: https://i.sstatic.net/UUFTC.png
  [3]: https://i.sstatic.net/h2uck.png