Practice Problems on Probability

(ECE302)

## Contents

- Definition of a set
- Set operations
- Conditional Probability
- Discrete Random Variables
- Continuous random variables
- Normalizing the probability mass function of a Gaussian random variable
- Obtaining the joint pdf from the marginal pdfs of two independent variables
- Compute a probability
- Find the CDF
- Compute the mean
- Compute the zero-th order moment of a Gaussian
- Compute the first order moment of a Gaussian
- Compute the second order moment of a Gaussian
- Comparing probabilities for different Gaussians
- Compute the probability that a meeting will occur
- Find the conditional probability density function
- Find the conditional probability density function (again)
- Find the conditional probability density function (conditioned on an event this time)
- Determine if X and Y independent from their joint density
- Recover the pmf corresponding to this characteristic function
- Obtain the characteristic function of an exponential random variable
- pdf of Y=aX+b
- Various Questions about a 2D Gaussian

- Random Processes

## Practice Problems written by students

- On conditional probability and/or independence
- On expectation and/or variance of a discrete random variable

## Quizzes

- Quiz 1 on the definition of a set
- Quiz 2 on proving De Morgan's law
- Quiz 3 set theoretic probability
- Quiz 4 Expectation of discrete random variable
- Quiz 5 cdf of Normal random variable (part1)
- Quiz 6 cdf of Normal random variable (part2)
- Quiz 7 Expectation of continuous random variable
- Quiz 8 Poisson Process

## Other practice Problems

- Various problems, with a short tutorial
- Distinguished versus undistinguished counting problems
- Summary of discrete probability, with some solved problems at the end
- Counting Subsets Practice Problems
- Counting Subsets Tutorial Example Problems
- Hillary and Barack, Lec. 3 on 8/29
- Disease testing, Lec. 3 on 8/29
- Switches, Lec. 5 on 9/8
- Car keys redistributed, Lec 10 on 9/19
- Coupon collection, Lec. 11 on 9/22
- Memoryless property of exponential, Lec 13 on 10/1
- When to arrive at the train station?_ECE302Fall2008sanghavi
- Finding area of a shape by random samples, Lec 14 on 10/3
- Conditional PDFs - random breaking of a stick, Lec 15 on 10/6_ECE302Fall2008sanghavi
- RV Coin Machine, Lec 17 on 10/10_ECE302Fall2008sanghavi
- PMF of x coordinate when uniformly dist. in a triangle, Lec 15 on 10/6_ECE302Fall2008sanghavi
- Example for continuous Probability Distributions. Vivek_ECE302Fall2008sanghavi
- Example finding covariance of coin flips, Lec 10/15_ECE302Fall2008sanghavi
- Exam Review Example 10/20_ECE302Fall2008sanghavi
- Markov Inequality Example_ECE302Fall2008sanghavi
- ML Estimate for Exponential RV_ECE302Fall2008sanghavi
- ML Estimate for Continuous RV on 10/31_ECE302Fall2008sanghavi
- ML Extimate explanation_ECE302Fall2008sanghavi
- Confidence Interval Bernoulli RV_ECE302Fall2008sanghavi
- Confidence Interval Example 11/07/08_ECE302Fall2008sanghavi
- Confidence Interval Explanation_ECE302Fall2008sanghavi
- MSE Example_ECE302Fall2008sanghavi
- Linear MMSE Estimator Example (12/1)_ECE302Fall2008sanghavi
- Hypothesis testting example 12/8_ECE302Fall2008sanghavi
- More on Hypothesis Testing 12/8_ECE302Fall2008sanghavi
- Various problems from Homework 2, Prof. Sanghavi
- Various problems from Homework 3, Prof. Sanghavi
- Various problems from Homework 4, Prof. Sanghavi
- Various problems from Homework 5, Prof. Sanghavi
- Various problems from Homework 6, Prof. Sanghavi
- Various problems from Homework 7, Prof. Sanghavi
- Various problems from Homework 8, Prof. Sanghavi
- Various problems from Homework 9, Prof. Sanghavi
- Various problems from Homework 10, Prof. Sanghavi