UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
FALL 2011
EE215-STOCHASTIC PROCESSES
HOMEWORK 1 SOLUTIONS
Problem:
You are traveling on a highway with constant speed. The highway is so unpopular that with probability
0.5, you will
Introduction to CDF and PDF
More About PDFs
Important Continuous RVs
Functions of RVs
Useful Bounds
Stochastic Processes
Lecture 3: Continuous Random Variables
Ertem Tuncel
Transforms
Introduction to CDF and PDF
More About PDFs
Important Continuous RVs
Fu
Denition and Examples
Probability Mass Function
Expected Value and Variance
Important Discrete RVs
Conditional PMFs
Stochastic Processes
Lecture 2: Discrete Random Variables
Ertem Tuncel
Denition and Examples
Probability Mass Function
Expected Value and V
Basic Denitions
Axioms of Probability
Conditional Probability
Independence
Sequential Experiments
Stochastic Processes
Lecture 1: Basic Concepts in Probability Theory
Ertem Tuncel
Basic Denitions
Axioms of Probability
Conditional Probability
Independence
Random Processes
Statistics as Functions of Time
Sum Processes
Poisson Processes
Stochastic Processes
Lecture 7: Random Processes
Ertem Tuncel
Gaussian Processes
Random Processes
Statistics as Functions of Time
Sum Processes
Poisson Processes
Random Proce
Sequences of RVs
Sums of RVs
Stochastic Processes
Lecture 6: Sums of Random Variables
and Convergence of Random Sequences
Ertem Tuncel
Laws of Large Numbers
Sequences of RVs
Sums of RVs
Laws of Large Numbers
Sequences of RVs
Let X1 , X2 , . . . , Xn , . .
Stationarity
Wide Sense Stationarity
Time Averages and Ergodic Theorems
Stochastic Processes
Lecture 8: Stationarity and Ergodicity
Ertem Tuncel
Stationarity
Wide Sense Stationarity
Time Averages and Ergodic Theorems
Stationary Random Processes
If the ran
Vector RVs
Expectation
Jointly Gaussian Vectors
Stochastic Processes
Lecture 5: Vector Random Variables
Ertem Tuncel
Vector RVs
Expectation
Jointly Gaussian Vectors
Vector Random Variables
A vector random variable X is a function that assigns a vector of
Power Spectral Density
Response to LTI Systems
Stochastic Processes
Lecture 9: Analysis and Processing of Random Signals
Ertem Tuncel
Power Spectral Density
Response to LTI Systems
Periodogram
Let X(t) be a WSS random process. Consider the Fourier transfo