ELEC 210: Probability and Random Processes in Engineering
Spring 2011
Instructor: Prof. Jun ZHANG Office: 2448 Tel: 2358 7050 Email: [email protected] Webpage: http:/www.ece.ust.hk/~eejzhang/
1
Elec 210
Elec210: Lecture 13
Multiple random variables (RVs) Joint probability mass function of two discrete RVs Marginal probability mass function
Elec210 Lecture 13
1
Vector Random Variables
A vector rando
Elec210 Lecture 12
MATLAB functions for continuous random variables Functions (Transformations) of a Random Variable
Elec210 Lecture 12
1
MATLAB Functions for Continuous RVs
Generating m by n arrays
Elec210 Lecture 11
o Expectation of Continuous Random Variables o Variance of Continuous Random Variables o Important Continuous Random Variables
Elec210 Lecture 11
1
Review: Expectation
Interpretati
Elec 210: Lecture 10
Single random variables: discrete, continuous and mixed
Continuous R.V. and Cumulative Distribution Function (CDF) Probability Density Function (PDF) Conditional CDFs and PDFs
El
Elec 210: Lecture 9
Important discrete random variables
Summary of variables you know:
Bernoulli Binomial Geometric Discrete Uniform
New random variable: Poisson
MATLAB commands for plotting prob
Elec 210: Lecture 8
Conditional Probability Mass Function Conditional Expected Value
Elec210 Lecture 8
1
Conditional Probability Mass Function
The effect of partial information about the outcome of
Elec 210: Lecture 7
Expectation of a random variable Expected value of a function of a random
variable
Variance of a random variable Moments of a random variable
The human brain weighs 1500 grams, o
Lecture 1 Model and Relative Frequency Practical Problem
Engineer
Solution
Models
Calculation
Mathematical solution
Relative Frequency
Axiomatic Approach
Limit Issues
1
Lecture 2: Axiomatic Approach
P
Elec 210: Lecture 6
Random Variables Equivalent events Discrete Random Variables Probability mass function Sir Isaac Newton and
We are more interested in a numerical attribute, i.e., numbers, of the
Elec 210: Lecture 5
Sequential Experiments e.g., the probability of having k heads when tossing the coin n times e.g., the probability of k heads before a tail comes up
Example: Bean Machine Game!
E
Elec 210: Lecture 4
Conditional Probability
Properties Total Probability Theorem Bayes Rule
Thus far, we have looked at the probability of events occurring individually, without regards to any other
Probability Model
Axiomatic approach
Practical Problem
Probability Model
Random Experiments
Elec210 Lecture 2
1
Elec 210: Lecture 2
Specifying Random Experiments
Sample spaces and events
Set Operat
5. Since
1
, L = constant
L
When L=1um, = 0.02V-1
When L=3um, ' =
L
L'
=
1u 0.02
= 0.00667
3u
In this question, we assume the transitor operates in saturation region when
VDS=1V. Also, we need to con