Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
1/24
Probability & Statistics
Continuous Random Variables 1
TRAN Hoang Tung
NGUYEN Minh Huong
NGUYEN Mai Chung
University of Science and Technology of Hanoi (USTH)
September 19, 2019

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF
Today

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF
Today
Continuous random variable

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF
Today
Continuous random variable
Probability density function (PDF)

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF
Today
Continuous random variable
Probability density function (PDF)
Expectation: mean, variance

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
2/24
The Course So Far
What we have learnt?
Probability model
Discrete random variable: PMF, mean, variance
Multiple random variables: joint, marginal PMF
Today
Continuous random variable
Probability density function (PDF)
Expectation: mean, variance
Cumulative distribution function (CDF)

Probability &
Statistics
Continuous
Random
Variables
Cumulative
Distribution
Functions
Common
Random
Variables
3/24
1
Continuous Random Variables
Probability Density Function
The Mean
Expected Value Rule
The Variance
2
Cumulative Distribution Functions
Continuous
Discrete
3
Common Random Variables
Exponential
Gaussian/Normal

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