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/
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Elec 210: Lecture 1
Course Details Models in Engineering Their
Elec210: Lecture 13
Multiple random variables (RVs) Joint probability mass function of two discrete RVs Marginal probability mass function
Elec210 Lecture 13
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Vector Random Variables
A vector random variable X is a function that assigns a vector
of rea
Elec210 Lecture 12
MATLAB functions for continuous random variables Functions (Transformations) of a Random Variable
Elec210 Lecture 12
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MATLAB Functions for Continuous RVs
Generating m by n arrays of random samples
unifrnd(a,b,m,n) exprnd(1/lambda,m,n
Elec210 Lecture 11
o Expectation of Continuous Random Variables o Variance of Continuous Random Variables o Important Continuous Random Variables
Elec210 Lecture 11
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Review: Expectation
Interpretation
The average value of a random variable if we repeat
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
Elec210 Lecture 10
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Random Variables: Review
A random
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 probability mass functions and generating discrete random v
Elec 210: Lecture 8
Conditional Probability Mass Function Conditional Expected Value
Elec210 Lecture 8
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Conditional Probability Mass Function
The effect of partial information about the outcome of a random
experiment on the probability of a discrete ra
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, on average.
Elec210 Lecture 7 1
Interesting Fact Einstei
Lecture 1 Model and Relative Frequency Practical Problem
Engineer
Solution
Models
Calculation
Mathematical solution
Relative Frequency
Axiomatic Approach
Limit Issues
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Lecture 2: Axiomatic Approach
Practical Problem
Axiomatic approach
Probability Models
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 outcome of the experiment, rather than cfw_tail, cfw_he
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!
Elec210 Lecture 5
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Sequential Experiments
Experiments
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 event. However, if we KNOW that a particular event occ
Elec 210: Lecture 3
Computing Probabilities using Counting Methods
Sample Size Computation and Examples Probabilities and Poker!
Elec210 Lecture 3
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Computing Probabilities Using Counting Methods
In experiments where the outcomes are equiprobable, we c
Probability Model
Axiomatic approach
Practical Problem
Probability Model
Random Experiments
Elec210 Lecture 2
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Elec 210: Lecture 2
Specifying Random Experiments
Sample spaces and events
Set Operations The Three Axioms of Probability
Corollaries
Prob
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 consider the Channel Length Modulation Effect.
(a) By I D