# Lecture16 - ECO220Y Lecture 16 Continuous Distribution Part...

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ECO220Y Lecture 16 Continuous Distribution Part 2 Continuous Distribution – Part 2 Migiwa Tanaka Reading: 8.2 and 8.4 (excluding χ 2 distributionሻ

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O tli Outline Continuous Distributions Uniform Distribution Triangle Distribution Normal Distribution Student t Distribution F Distribution study from textbook.
N l Di t ib ti 0 1 0.2 Normal Distribution 0 0.1 Why is it important? It has convenient features for theoretical analysis. It i k th t di t b bilit di t ib ti It is known that some discrete probability distributions can be approximated by Normal distribution. It i k th t f d i bl ill t ll It is known that sum of random variables will eventually follow Normal distribution as the number of random variables increases (Central Limit Theorem) variables increases. (Central Limit Theorem) It is also called Bell shape curve Gaussian Distribution

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N l Di t ib ti F l D fi iti Normal Distribution- Formal Definition Probability Density Function for Normal Random Variable X with mean μ and variance 2 is 2 2 1 1 ) ( x f 2 e x . ,  x X ~N(μ, 2 ) implies random variable X is distributed to normal distribution of mean μ and variance 2 What are the parameter of this distribution?