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Expectation of Random Variables
September 17 and 22, 2009
1
Discrete Random Variables
Let x1 , x2 , xn be observation, the empirical mean,
x
=
1
(x1 + x2 + xn ).
n
So, for the observations, 0, 1, 3, 2, 4, 1, 2, 4, 1, 1, 2, 0, 3,
24
.
13
x
=
We could also

Statistics 116 - Fall 2004
Theory of Probability
Assignment # 6
Due Friday, November 05
Solution prepared by Xiaohu Zhang, zhangxh@stat.stanford.edu
Nov 5, 2004
Q. 1)
Q. 2)
(Ross #5.19)
Answer
Let X be a normal random variable with mean 12 and
variance 4.

Friday, September 02, 2016
9:08 AM
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10:27 AM
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10:49 AM
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Midterm Exam for
ELE606 Probablisitic Methods (Fall 2015)
9:30-11:30pm, Friday October 16, 2015
NAME
Closed book closed note. One cheat sheet allowed.
If additional papers are used, write your name on each of them and mark clearly the problem
number on

ELE606 (Fall 2016) Homework # 1
Due Friday September 9 in class
1. 1.2
2. 1.4
3. 1.5
4. 1.6
5. A random experiment consists of drawing two balls with replacement from a urn that contains 8
balls numbered 1, ., 8. Let S denote the sum of the two numbers on

Linear combination of Normal Random Variables
Linear Function of a Normal Random Variable
If X ~ N ( , 2 ) and a and b are constants, then
Y = aX + b ~ N (a + b, a 2 2 )
Linear Combinations of Independent Normal Random Variable
If X i ~ N ( i , i2 ) , 1 i

ELE606 (Fall 2016) - Homework # 4
Due Friday October 21 in class
1. 2.30
2. 2.32
3. 2.33(a,b)
4. 3.4
5. A committee of three judges is randomly selected from among ten judges. Four of the ten
judges are tough; the committee is tough if at least two of the

ELE606 (Fall 16) Homework # 2
Due Friday September 23rd in class
1. 1.38.
2. 1.39.
3. 1.46.
4. 1.55.
5. A rolls two dice and wins if theres at least one 6. B rolls four dice and wins if there are at least
two 6s. Which one has greater probability to win?