10: The Normal (Gaussian) Distribution

[Pages:53]10: The Normal (Gaussian) Distribution

Lisa Yan April 27, 2020

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Quick slide reference

3 Normal RV 15 Normal RV: Properties 21 Normal RV: Computing probability 30 Exercises

Lisa Yan, CS109, 2020

10a_normal 10b_normal_props

10c_normal_prob LIVE

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10a_normal

Normal RV

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Today's the Big Day

Today

Lisa Yan, CS109, 2020

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Normal Random Variable

def An Normal random variable is defined as follows:

~(, 2)

Support: -,

PDF Expectation Variance

= 1 - - 2/22 2

= Var = 2

Other names: Gaussian random variable

mean variance

~(, 2)

Lisa Yan, CS109, 2020

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Carl Friedrich Gauss

Carl Friedrich Gauss (1777-1855) was a remarkably influential German mathematician.

Did not invent Normal distribution but rather popularized it

Lisa Yan, CS109, 2020

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Why the Normal?

? Common for natural phenomena: height, weight, etc.

? Most noise in the world is Normal ? Often results from the sum of many

random variables ? Sample means are distributed normally

Lisa Yan, CS109, 2020

That's what they want you to believe...

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Why the Normal?

? Common for natural phenomena: height, weight, etc.

? Most noise in the world is Normal

? Often results from the sum of many random variables

? Sample means are distributed normally

Actually log-normal

Just an assumption

Only if equally weighted

(okay this one is true, we'll see this in 3 weeks)

Lisa Yan, CS109, 2020

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