Example of a random variable
Random Experiment: Roll a six-sided die.
Sample
space
𝑠1
1
𝑠2
2
𝑠3
3
𝑠4
4
𝑠5
5
𝑠6
𝑋2
-1
-2
-3
-4
-5
-6
𝑋3
1
4
9
16
25
36
2𝑋1
2
4
6
8
10
12
𝑋1 + 𝑋3
2
6
12
20
30
42
𝑋1
6
𝐸 [𝑋] = 𝑝(𝑠1 )𝑋(𝑠1 ) + 𝑝(𝑠2 )𝑋(𝑠2 ) + 𝑝(𝑠3 )𝑋(𝑠3 ) + 𝑝(𝑠4 )𝑋(𝑠4 ) + 𝑝(𝑠5 )𝑋(𝑠5 ) + 𝑝(𝑠6 )𝑋(𝑠6 )
𝐸 [𝑋 2 ] = 𝑝(𝑠1 )𝑋 2 (𝑠1 ) + 𝑝(𝑠2 )𝑋 2 (𝑠2 ) + 𝑝(𝑠3 )𝑋 2 (𝑠3 ) + 𝑝(𝑠4 )𝑋 2 (𝑠4 ) + 𝑝(𝑠5 )𝑋 2 (𝑠5 ) + 𝑝(𝑠6 )𝑋 2 (𝑠6 )