ELEC2817/ELEC3847 Probability and Statistics in

Engineering (TUTORIAL 1)---8 Sept 2015

Class schedule:

[1] Tuesdays; Time: 12:30pm - 1:20pm; Venue: M124

[2] Tuesdays; Time: 1:30pm - 2:20pm; Venue: JL-G03

Tutor : Michael Chan Email : cychan@eee.hku.hk

Phone : 2859 2699 Office : CB-514

Tutorial website : http://www.eee.hku.hk/~cychan

p.s. All solutions will be posted on Moodle!!!!

Tutorial material will be posted on my Tutorial website!!!

ELEC 2817 / ELEC3847---Practice Exercise 0

Solution:

ELEC 2817 / ELEC3847---Practice Exercise 0

Solution:

ELEC 2817 / ELEC3847---Practice Exercise 0

Solution:

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

0

311

242

113

0

:equation sticcharacteri The

IA-

e.g.

(cofactor expansion)

0)2)(2)(6(

0242810

0)]4(2[]2)3(2[]2)3)(4)[(3(

011

42)1(

31

22)1(

31

24)3(

23

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

ELEC 2817 / ELEC3847---Practice Exercise 0

Conditional Probability

Total Probability

[Ex. 1]

We are given three coins: one has heads in both

faces, the second has tails in both faces, and the

third has a head in one face and a tail in the other.

We choose a coin at random, toss it, and the result

is tail. What is the probability that the opposite face

has a head?

up) came P(tail

up) came tailandcoin P(1H1Tup) came tail\coin P(1H1T

Conditional probability

Tree diagram for Ex.1

3

1

13

10

3

1

2

1

3

1

2

1

3

1

up) came P(tail

up) came tailandcoin P(1H1Tup) came tail\coin P(1H1T

:yprobabilit lconditiona The

3

1

13

10

3

1

2

1

3

1

2

1

3

1

2T)\P(2T)P(T2H)\P(2H)P(T1H1T)\P(1H1T)P(T

1H1T)\P(1H1T)P(TT)\P(1H1T

:Theorem Bayes'

[Ex.2]

(a) A hat contains m balanced coins and n double-

headed coins. One coin is selected at random

and tossed. You are allowed to see only the up-

face, which is heads. What is the probability that

the hidden face is also heads?

(b) A hat contains m balanced coins and n double-

headed coins. Two coins are selected at random

and tossed. You are allowed to see only the up-

faces, which are both heads. What is the

probability the hidden faces are

(i) both heads,

(ii) both tails?

Tree diagram for Ex.2(a)

)(2

2

12

1

)(

(a)

nm

nm

nm

n

nm

m

HP

nm

n

nm

nm

nm

n

P

P

P

2

2

)(2

2

1

(H)

H) head-(double

H)\head-(double

Tree diagram for Ex.2(b)

1

1

)1)((

2

11

1

1

3

2

1

nm

n

nm

nP

nmnm

mn

nm

m

nm

n

nm

n

nm

mP

nm

m

nm

mP

)1)((4

4)2(

)1)((

)1(

)1)((2

2

)1)((4

)1(

2

1

4

1)2H(

2

321

nmnm

nmnm

nmnm

nn

nmnm

mn

nmnm

mm

PPPP

nmnm

mm

P

P

P

nmnm

nn

P

P

P

4)2(

)1(

)2H(

4

1

)2H\coinsfair 2( (ii)

4)2(

)1(4

)2H(

)2H\headed-double( (i)

2

1

2

3