Conditional distribution of random variables

1
Conditional Distribution.
2
Conditional Distribution
3
Example
1 2 3
1 0 1/8 1/16
2 1/8 1/16 1/8
3 2/8 0 2/8
y
x
4
Answer
1 2 3
1 0 1/8 1/16 3/16
2 1/8 1/16 1/8 5/16
3 2/8 0 2/8 1/2
3/8 3/16 7/16
y
x
5
Continue
1 2 3
1 0 1/8 1/16 3/16
y
x




6
Continue
1 2 3
2 1/8 1/16 1/8 5/16
y
x




7
Continue
1 2 3
3 2/8 0 2/8 1/2
y
x




8
Continue
1 2 3



9
Continue
1
1 0
2 1/8
3 2/8
3/8
y

1
2
3
x
10
Continue
2
1 1/8
2 1/16
3 0
3/16
y

1
2
3
x
11
Continue
3
1 1/16
2 1/8
3 2/8
7/16
y

1
2
3
x
12
Continue

1
2
3
13
Assignment
14
Answer X on Y i.e. f(x/y)
1 2 3 4 5 6
1 0 0 0 0 0
1 0 0 0 0 0
2/3 1/3 0 0 0 0
1/2 1/2 0 0 0 0
2/5 2/5 1/5 0 0 0
1/3 1/3 1/3 0 0 0
0 2/5 2/5 1/5 0 0
0 0 1/2 1/2 0 0
0 0 0 2/3 1/3 0
0 0 0 0 1 0
0 0 0 0 0 1
15
Continue..r Y on X i.e. f(y/x)
2 3 4 5 6 7 8 9 10 11 12
1/11 2/11 2/11 2/11 2/11 2/11 0 0 0 0 0
0 0 1/9 2/9 2/9 2/9 2/9 0 0 0 0
0 0 0 0 1/7 2/7 2/7 2/7 0 0 0
0 0 0 0 0 0 1/5 2/5 2/5 0 0
0 0 0 0 0 0 0 0 1/3 2/3 0
0 0 0 0 0 0 0 0 0 0 1
16
Conditional Distribution
17
Example-
18
Answer
19
Continue
20
Independent Random Variables.
21
Example-
22
Answer
0 1
0 1/4 1/4 1/2
1 1/4 1/4 1/2
1/2 1/2
y
x
23
Continue
24
Assignment
25
Thank You ALL
Make Presentation much more fun