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Probability and Statistics for Engineers from Imperial College London
Learn about Probability and Statistics for Engineers. Module given at Imperial College London to second year undergraduate students in electrical and electronic engineering.
Probability and Statistics for Engineers: sets, events, axioms of probability, random variables, probability mass function, probability density function, cumulative distribution function, expectation and variance, single discrete or continuous random variable, systems and component reliability, multiple discrete or continuous random variables, jointly distributed random variables, change of variables, moments, moment generating function, conditional probability, conditional expectation, conditional variance, law of large numbers, central limit theorem, basic properties of estimators, method of moments, and maximum likelihood estimators.
- Probability and Statistics for Engineers (Part 1 of 8): set theory, events, axioms of probability
- Probability and Statistics for Engineers (Part 2 of 8): Bayes Theorem, discrete random variables
- Probability and Statistics for Engineers (Part 3 of 8): discrete and continuous random variables
- Probability and Statistics for Engineers (Part 4 of 8): continuous random variables
- Probability and Statistics for Engineers (Part 5 of 8): jointly distributed random variables
- Probability and Statistics for Engineers (Part 6 of 8): jointly distributed random variables
- Probability and Statistics for Engineers (Part 7 of 8): change of variables, LLN, CLT, estimators
- Probability and Statistics for Engineers (Part 8 of 8): method of moments, maximum likelihood
- Probability and Statistics for Engineers - Exam Questions
Probability and Statistics for Engineers (Part 1 of 8): set theory, events, axioms of probability
0:00 Introduction
5:07 what is probability? What is statistics?
10:15 Sets
15:58 Union of sets
19:11 Intersection of sets
24:44 Disjoint sets
26:54 Partition
29:16 Complement of set
32:06 Difference of sets
35:53 Disjoint union
42:14 De Morgan's law
54:36 Sample space and events
1:04:08 Axioms of probability
1:09:28 Probability of union
Probability and Statistics for Engineers (Part 2 of 8): Bayes Theorem, discrete random variables
Axioms of probability, conditional probability, independence, partition, total probability, Bayes Theorem, discrete random variables, probability mass function (PMF), cumulative distribution function (CDF), expectation, variance.
2:20 Summary of previous lecture
7:30 Conditional probability
12:42 Multiplication law
14:47 two independent events
18:25 mutually independent events
32:38 Probability tables
39:00 Law of total probability
53:00 Bayes theorem
1:01:38 Discrete random variable
1:04:55 Probability mass function (PMF)
1:10:38 Cumulative distribution function (CDF)
1:16:00 Expectation / theoretical mean
1:26:12 Variance and standard deviation
Probability and Statistics for Engineers (Part 3 of 8): discrete and continuous random variables
Discrete and continuous random variables, probability distribution (Uniform, Binomial, Geometric, Poisson), probability mass function (PMF), cumulative distribution function (CDF), expectation, variance, probability density function (PDF).
0:47 Summary of previous lecture
11:10 Uniform distribution
16:54 Binomial distribution
42:52 Geometric distribution
47:35 Poisson distribution
1:07:17 Continuous random variable
1:09:10 Probability density function (PDF)
1:15:22 Cumulative distribution function (CDF)
1:23:50 Expectation
1:27:25 Variance and standard deviation
Probability and Statistics for Engineers (Part 4 of 8): continuous random variables
Continuous random variables, probability distribution (Uniform, Exponential, Normal/Gaussian, Chi-Square, Log-Normal), change of variable: one function of one random variable, Chebyshev's Inequality, systems and component reliability.
0:41 Summary of previous lecture
2:53 Uniform distribution
7:17 Exponential distribution
23:29 Change of variable (one to one)
34:30 Normal / Gaussian distribution
1:12:12 Chi square distribution
1:20:22 Log normal distribution
1:26:00 Chebyshev's inequality
1:37:25 Systems and component reliability
Probability and Statistics for Engineers (Part 5 of 8): jointly distributed random variables
Systems and component reliability, reliability function, hazard rate, Weibull distribution, jointly distributed random variables, Joint PMF, Joint PDF, marginals, independent random variables, conditional PMF/PDF, conditional expectation.
0:36 Summary of previous lecture
9:30 random time to failure
10:00 Failure time distribution
11:00 Failure time density
11:30 Reliability function.
12:22 Hazard rate
16:10 Cumulative hazard function
26:32 Mean time to failure
28:30 Jointly distributed random variables
30:25 Joint cumulative distribution function
32:30 Joint probability mass function
36:23 Marginal probability mass function
40:30 Joint probability density function
46:50 Marginal probability density function
1:00:05 Independent random variables
1:08:32 Conditional PMF/PDF
1:15:50 Expectation
1:28:36 Conditional expectation
Probability and Statistics for Engineers (Part 6 of 8): jointly distributed random variables
Conditional variance, covariance, correlation, joint Normal (Gaussian) distribution, moments, moment generating function, characteristic function, relationship with Fourier Transform, sums of random variables.
0:57 Summary of previous lecture
4:52 Conditional variance
18:46 Covariance
33:25 Uncorrelated random variables
43:35 Correlation
51:50 Joint Normal / Gaussian distribution
59:30 Moments
1:03:35 Moment generating function
1:32:45 Characteristic function
1:37:30 Sums of random variables
Probability and Statistics for Engineers (Part 7 of 8): change of variables, LLN, CLT, estimators
Change of variables: one function of two random variables, two functions of two random variables, Rayleigh distribution, Law of Large Numbers (LLN), Central Limit Theorem (CLT), Statistics and sampling distributions, estimator, properties of estimators, biased/unbiased estimator, minimum variance.
0:00 Summary of previous lecture
5:50 Binomial and Bernoulli
14:46 Change of variables: two to one
16:10 PDF of the maximum of two random variables
21:00 PDF of the sum of two random variables
33:34 Change of variables: two to two
44:04 Rayleigh distribution
54:20 Law of large number and central limit theorem
1:12:10 Statistics
1:16:20 Random sample
1:21:50 Estimator
1:24:50 Unbiased vs biased estimator
1:38:57 Minimum variance unbiased estimator
Probability and Statistics for Engineers (Part 8 of 8): method of moments, maximum likelihood
Statistics, estimators, mean squared error, method of moments, maximum likelihood estimation.
1:00 Summary of previous lecture
8:52 Mean squared error (MSE)
16:55 Method of moment estimator
32:02 Maximum likelihood estimator
Probability and Statistics for Engineers - Exam Questions (Part 1 of 2)
Part 1 of Exam Questions
Probability and Statistics for Engineers - Exam Questions (Part 2 of 2)
Part 2 of Exam Questions
#probability #statistics
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ACT Math Prep Study Guide Review
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How to Perform A Hypothesis Test Of independence in Statistics
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Introduction to The Chi Square Test In Statistics
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Introduction Into Matched Or Paired Samples In Statistics
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How to Perform Hypothesis Testing with Two Sample Means in Statistics
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How to Solve Hypothesis Testing Problems with Proportions
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How to Use The P-value To Solve Problems with Hypothesis Testing
This statistics video explains how to use the p-value to solve problems associated with hypothesis testing. When the p-value is less than alpha, you should reject the null hypothesis and vice versa. This video discusses when you should use a one tailed test compared to a two tailed test. It contains two example problems that illustrates how to use the p-value method to determine if you should reject or not reject the null hypothesis.
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#statistics #probability #maths #mathematics
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Statistics Tutorial: Hypothesis Testing Problems
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How to Calculate Test Statistic for Means and Population Proportions
This statistics video tutorial provides the formulas for calculating the test statistic for the population mean and population proportion. This includes the z-statistic and t-statistic.
