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[[Category:ECE302]] | [[Category:ECE302]] | ||
| − | [[Category: | + | [[Category:probability]] |
| + | [[Category:Problem_solving]] | ||
| − | =[ | + | <center> |
| + | <font size= 4> | ||
| + | [https://www.projectrhea.org/learning/practice.php Practice Problems] on Probability | ||
| + | </font size> | ||
| + | |||
| + | ([[ECE302]]) | ||
| + | </center> | ||
| + | ---- | ||
| + | ==Collectively solved problems related to Probability== | ||
| + | *Definition of a set | ||
| + | **[[Practice_Question_definition _set_ECE302S13Boutin|Do these signals form a set?]] | ||
| + | *Set operations | ||
| + | **[[Practice_Question_definition_set_union_ECE302S13Boutin|Union of two sets]] | ||
| + | **[[Practice_Question_definition_set_union_2_ECE302S13Boutin|Union of two sets (again)]] | ||
| + | *Conditional Probability | ||
| + | **[[Practice_Question_Monty_Hall_ECE302S13Boutin|Explain the Monty Hall problem using conditional probability]] | ||
| + | *Discrete Random Variables | ||
| + | **[[Practice_Question_probability_normalization_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]] | ||
| + | *Continuous random variables | ||
| + | **[[Practice_Question_gaussian_normalization_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]] | ||
| + | **[[Practice_Question_joint_from_marginals_independent_variables_ECE302S13Boutin|Obtaining the joint pdf from the marginal pdfs of two independent variables]] | ||
| + | **[[Practice_Question_linear_random_variable_probability_ECE302S13Boutin|Compute a probability]] | ||
| + | **[[Practice_Question_uniform_random_variable_CDF_ECE302S13Boutin|Find the CDF]] | ||
| + | **[[Practice_Question_uniform_random_variable_mean_ECE302S13Boutin|Compute the mean]] | ||
| + | **[[Practice_Question_moment_order_zero_Gaussian_ECE302S13Boutin|Compute the zero-th order moment of a Gaussian]] | ||
| + | **[[Practice_Question_moment_order_one_Gaussian_ECE302S13Boutin|Compute the first order moment of a Gaussian]] | ||
| + | **[[Practice_Question_moment_order_two_Gaussian_ECE302S13Boutin|Compute the second order moment of a Gaussian]] | ||
| + | **[[Practice_Question_comparing_probabilities_Gaussians_ECE302S13Boutin|Comparing probabilities for different Gaussians]] | ||
| + | **[[Practice_Question_probability_meeting_occurs_ECE302S13Boutin|Compute the probability that a meeting will occur]] | ||
| + | **[[Practice_Question_find_conditional_pdf_ECE302S13Boutin|Find the conditional probability density function]] | ||
| + | **[[Practice_Question_find_conditional_ellipse_ECE302S13Boutin|Find the conditional probability density function (again)]] | ||
| + | **[[Practice_Question_find_conditional_event_ECE302S13Boutin|Find the conditional probability density function (conditioned on an event this time)]] | ||
| + | **[[Practice_Question_independence_ECE302S13Boutin|Determine if X and Y independent from their joint density]] | ||
| + | **[[Practice_Question_characteristic_function_ECE302S13Boutin|Recover the pmf corresponding to this characteristic function]] | ||
| + | **[[Practice_Question_characteristic_function_exponential_random_variable_ECE302S13Boutin|Obtain the characteristic function of an exponential random variable]] | ||
| + | **[[Practice_Question_characteristic_linear_function_random_variable_ECE302S13Boutin|pdf of Y=aX+b ]] | ||
| + | **[[Practice_Question_2D_Gaussian_ECE302S13Boutin|Various Questions about a 2D Gaussian]] | ||
| + | *Random Processes | ||
| + | **[[Practice_Question_what_is_stationary_increment_property_sum_process_ECE302S13|the stationary increment property of a sum process]] | ||
| + | ---- | ||
| + | ==Practice Problems written by students== | ||
| + | *On conditional probability and/or independence | ||
| + | **[[EC1-Boldt]] | ||
| + | **[[ECE_302-Extra_Credit-_Zimmerman]] | ||
| + | **[[Tetris_Independence_-_ECE302]] | ||
| + | **[[ECE302_First_Bonus_point_opportunity_yanwen_jin]] | ||
| + | **[[ECE302_EC1_Woo]] | ||
| + | **[[BonusProblem_Zhenming_Zhang]] | ||
| + | **[[ECE_302_EC_Desai]] | ||
| + | **[[ECE302_BonusProblem_Ruofei_Chen]] | ||
| + | **[[ECE302_Problem_Zihui_Liu]] | ||
| + | **[[Green26_ece302_ec1| Pixels (alec green)]] | ||
| + | *On expectation and/or variance of a discrete random variable | ||
| + | **[[ThirdBonusDude91|Dude91's Question]] | ||
| + | **[[ECE302_EC2_Woo]] | ||
| + | ---- | ||
| + | ==Quizzes== | ||
| + | *[[quiz1_set_definition_ECE302_S13_Boutin|Quiz 1 on the definition of a set]] | ||
| + | *[[quiz2_set_operation_prove_De_Morgan_Law_ECE302_S13_Boutin|Quiz 2 on proving De Morgan's law]] | ||
| + | *[[quiz3_set_theory_probability_S13_Boutin|Quiz 3 set theoretic probability]] | ||
| + | *[[quiz4_expectation_discrete_RV_ECE302_S13_Boutin|Quiz 4 Expectation of discrete random variable]] | ||
| + | *[[quiz5_cdf_GaussianRV_ECE302_S13_Boutin|Quiz 5 cdf of Normal random variable (part1)]] | ||
| + | *[[quiz6_cdf_GaussianRV2_ECE302_S13_Boutin|Quiz 6 cdf of Normal random variable (part2)]] | ||
| + | *[[quiz7_expectation_continuousRV_ECE302_S13_Boutin|Quiz 7 Expectation of continuous random variable]] | ||
| + | *[[quiz8_Poisson_process_ECE302_S13_Boutin|Quiz 8 Poisson Process]] | ||
| + | ---- | ||
| + | ==Other practice Problems== | ||
*[[Mysteries_of_probability_MA375S12Walther|Various problems, with a short tutorial]] | *[[Mysteries_of_probability_MA375S12Walther|Various problems, with a short tutorial]] | ||
*[[Distinguished/Indistinguished_Problem|Distinguished versus undistinguished counting problems]] | *[[Distinguished/Indistinguished_Problem|Distinguished versus undistinguished counting problems]] | ||
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* [[homework10_ECE302Fall2008sanghavi|Various problems from Homework 10, Prof. Sanghavi]] | * [[homework10_ECE302Fall2008sanghavi|Various problems from Homework 10, Prof. Sanghavi]] | ||
---- | ---- | ||
| − | + | [[ECE302|Back to ECE302: "Probabilistic Methods in ECE"]] | |
| − | + | ||
Latest revision as of 18:17, 23 February 2015
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
