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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**

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

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

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

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

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

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

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

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

Part 1 of Exam Questions

Part 2 of Exam Questions

#probability #statistics

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#statistics #probability #maths #mathematics

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