## 課程信息

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## Conditional probability and Independence

13 個視頻 （總計 123 分鐘）
13 個視頻
Conditional probability. Motivation and Example13分鐘
Conditional probability. Definition8分鐘
Independent events. Example7分鐘
Independent events. Definition12分鐘
Mosaic Plot. Visualization of conditional probabilities and Independence11分鐘
Using independence to find probabilities. Examples10分鐘
Pairwise and mutual independence12分鐘
Bernoulli Scheme11分鐘
Law of total probability14分鐘
Bayes's rule4分鐘
Python for conditional probabilities9分鐘
Conditional probability. Highlights3分鐘
7 個練習
Coins, dices and conditional probability20分鐘
Independence and intersection5分鐘
Fair coin and independence6分鐘
Mutual independence conditions5分鐘
Call center total probability5分鐘
Bayes's taxi companies5分鐘
2

## Random variables

15 個視頻 （總計 150 分鐘）
15 個視頻
Examples of random variables11分鐘
Mathematical definition of random variable5分鐘
Probability distribution and probability mass function (PMF)15分鐘
Binomial distribution10分鐘
Expected value of random variable. Motivation and definition14分鐘
Expected value example and calculation11分鐘
Expected value as best prediction15分鐘
Variance of random variable. Motivation and definition7分鐘
Discrete random variables with infinite number of values11分鐘
Saint Petersburg Paradox. Example of infinite expected value6分鐘
Geometric and Poisson distributions6分鐘
Generating discrete random variables with Python11分鐘
Numpy, scipy and matplotlib for generation and visualization of common distributions12分鐘
Random variables. Highlights3分鐘
3 個練習
Expected value exercises20分鐘
Variance skill test25分鐘
Random variables and geometric series10分鐘
3

## Systems of random variables; properties of expectation and variance, covariance and correlation.

16 個視頻 （總計 127 分鐘）
16 個視頻
Linear transformations of random variables8分鐘
Linearity of expected value6分鐘
Symmetric distributions and their expected values6分鐘
Functions of random variables5分鐘
Properties of variance6分鐘
Sum of random variables. Expected value and variance8分鐘
Joint probability distribution12分鐘
Marginal distribution8分鐘
Independent random variables7分鐘
Another example of non-independent random variables8分鐘
Expected value of product of independent random variables8分鐘
Variance of sum of random variables. Covariance11分鐘
Properties of covariance10分鐘
Correlation of two random variables7分鐘
Systems of random variables. Highlights3分鐘
7 個練習
PMF of linear transformations5分鐘
Expectation properties5分鐘
Joint distribution skill test15分鐘
Joint PMF10分鐘
Variance of Binomial random variable5分鐘
Covariance for a dice roll5分鐘
Correlation quiz5分鐘
4

## Continuous random variables

16 個視頻 （總計 156 分鐘）
16 個視頻
Continuous random variables. Motivation and Example10分鐘
Probability density function (PDF)9分鐘
Cumulative distribution function (CDF)13分鐘
Properties of CDF6分鐘
Examples of probability density functions10分鐘
Histogram as approximation to a graph of PDF11分鐘
Expected value of continuous random variable9分鐘
Variance of continuous random variable. Properties of expected value and variance7分鐘
Transformations of continuous random variables and their PDFs11分鐘
Joint CDF and PDF. Level charts. Marginal PDF10分鐘
Independence, covariance and correlation of continuous random variables9分鐘
Mixed random variables. Example11分鐘
Generating and visualizing continuous random variables with Python10分鐘
Generating correlated random variables with Python11分鐘
8 個練習
CDF of discrete random variable7分鐘
PDF and CDF skill test15分鐘
Finding expectation with PDF5分鐘
Finding variance with PDF5分鐘
Expectation of a function of random variable2分鐘
PDF skill test7分鐘
Variance of sum of Gaussian random variables5分鐘
Distinguishing random variables3分鐘

## 關於 Mathematics for Data Science 專項課程

Behind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.... ## 常見問題

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