Statistical  Thinking:Monte  Carlo  Simulation

Industrial  AI  Lab.

Probability  of  Having  Head  with  a  Fair  Coin• Head  1  and  Tail  0

2

Expectation

3

• Q:  The  Expected  Number  of  Trials  up  to  the  First  Hitting  H  ?

Expectation

4

• Q:  The  Expected  Number  of  Trials  up  to  the  First  Hitting  H  ?

Expectation

• Remark:  how  to  compute

5

Expectation• Or

6

Integration

• Question  :  how  to  solve  integration  with  computers  ?

7

Integration

8

Integration• Question:  another  method  ?  (use  randomness)

9

Monte  Carlo  Simulation• It  is  known  asMonte  Carlo  simulation⟹ extremely  powerful⟹ can  apply  to  many,  many,  many  (engineering)  problems

10

Integration:  Monte  Carlo  Simulation

11

Compute  𝝅 statistically

12

Compute  𝝅 statistically

13

Compute  𝝅 statistically

14