Lecture16 - ECO220Y Lecture 16 Continuous Distribution Part...

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ECO220Y Lecture 16 ontinuous Distribution art 2 Continuous Distribution – Part 2 Migiwa Tanaka Reading: 8.2 and 8.4 (excluding χ 2 distributionሻ
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Outline ontinuous Distributions Continuous Distributions Uniform Distribution iangle Distribution Triangle Distribution Normal Distribution Student t Distribution F Distribution study from textbook.
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1 0.2 Normal Distribution 0 0.1 hy is it important? Why is it important? It has convenient features for theoretical analysis. 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. th t f d i b l ill t ll It is known that sum of random variables will eventually follow Normal distribution as the number of random riables creases (Central Limit Theorem) variables increases. (Central Limit Theorem) It is also called Bell shape curve Gaussian Distribution
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Normal Distribution- Formal Definition robability Density Function for Normal Random Variable Probability Density Function for Normal Random Variable X with mean μ and variance 2 is 2 2 1 1 x 2 ) ( e x f . ,  x X ~N(μ, 2 ) implies random variable X is distributed to normal distribution of mean μ and variance 2 hat are the parameter of this distribution? What are the parameter of this distribution?
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Normal Distribution- Formal Definition robability Density Probability Density Function xf ( x ) 2 -4 0.000134 -3 0.004432 2 1 2 1 ) ( x e x f -2 0.053991 -1 0.241971 398942 . ,  x Suppose μ=0 0 0.398942 1 0.241971 053991 σ 2 =1 2 0.053991 3 0.004432 000134 4 0.000134 2 1828 1 14159 . 3 2 1 ) ( x x f   71828 . 2
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Plotting Normal Density .4 xf ( x ) -4 0.000134 .3 -3 0.004432 -2 0.053991 .2 -1 0.241971 0 0.398942 .1 1 0.241971 2 0.053991 0 -4 -3 -2 -1 0 1 2 3 4 3 0.004432 4 0.000134 -4 -3 -2 -1 0 1 2 3 4 What is the range of this distribution?
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Normal Distribution Shape and Parameters -- Mean .6 Which distribution has the largest mean?
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This note was uploaded on 03/01/2011 for the course ECON 220 taught by Professor Tanaka during the Spring '11 term at University of Toronto.

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Lecture16 - ECO220Y Lecture 16 Continuous Distribution Part...

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