Math 19b: Linear Algebra with Probability Oliver Knill, Spring 2011
Lecture 10: Worksheet
Random variables
1We throw 3 dice and define the random variable X(ω) which as
the maximal value of the three dice. Draw the probability distribu-
tion. This means we want to find the probabilities P[X= 1],P[X=
2],P[X= 3],P[X= 4],P[X= 5] and P[X= 6].
2Find the mean
m= E[X] = 1P[X= 1] + 2P[X= 2] + ... + 6P[X= 6]
of the random variable Xfound in the previous problem.
3Time will probably not permit this during class but find the vari-
ance of X
Var[X] = (1−m)2P[X= 1]+(2−m)2P[X= 2]+...+(6−m)2P[X= 6]
4Find the standard deviation σ[X] = qVar[X].
1
2
3
4
5
6
10
20
30
40