### Problem1
#### 1.1-1.2
- f=3%
[PASTE IMAGE HERE]
erroneous bit: 63176
error rates: 3.012466%

- f=10%
[PASTE IMAGE HERE]
erroneous bit: 210091
error rates: 10.017920%

- f=30%
[PASTE IMAGE HERE]
erroneous bit: 629950
error rates: 30.038357%

#### Problem2
##### 2.1-2.2
- f=3%
[PASTE IMAGE HERE]
erroneous bit: 2702
error rates: 0.128841%
ratio of correctable Error: 46.922799%

- f=10%
[PASTE IMAGE HERE]
erroneous bit: 29019
error rates: 1.383734%
ratio of correctable Error: 40.491135%

- f=30%
[PASTE IMAGE HERE]
erroneous bit: 226002
error rates: 10.776615%
ratio of correctable Error: 24.450158%

#### 2.3
- In case of f=3%
- problem1
error rates: 3.012466%
- R3
error rates: 0.128555%

The error rate decreased significantly.

#### 2.4
##### 2.4.1
f=0.3%
##### 2.4.2
The reason is that voting affected by f. If f increases, each voting bits is affected by noise. As the result, ratio of correctable error decreases. The opposite is also true.

#### Problem3
##### 3.1

##### 3.2-3.3
- f=10%, R=5
[PASTE IMAGE HERE]
erroneous bit: 9074
error rates: 0.432682%

- f=10%, R=7
[PASTE IMAGE HERE]
erroneous bit: 2914
error rates: 0.138950%

##### 3.4

#### Problem4
##### 4.1-4.2
- f=3%
[PASTE IMAGE HERE]
erroneous bit: 31869
error rates: 1.519632%

- f=10%
[PASTE IMAGE HERE]
erroneous bit: 111590
error rates: 5.321026%

- f=30%
[PASTE IMAGE HERE]
erroneous bit: 358403
error rates: 17.089987%

##### 4.3