The normal distrib u tion FOU N DATION S OF P R OBABIL ITY IN R Da - - PowerPoint PPT Presentation

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May 29, 2023 346 likes •542 views

The normal distrib u tion FOU N DATION S OF P R OBABIL ITY IN R Da v id Robinson Chief Data Scientist , DataCamp Flipping 10 coins flips <- rbinom(100000, 10, .5) FOUNDATIONS OF PROBABILITY IN R Flipping 1000 coins flips <- rbinom(100000,

SLIDE 1

The normal distribution

FOU N DATION S OF P R OBABIL ITY IN R

David Robinson

Chief Data Scientist, DataCamp

SLIDE 2

FOUNDATIONS OF PROBABILITY IN R

Flipping 10 coins

flips <- rbinom(100000, 10, .5)

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FOUNDATIONS OF PROBABILITY IN R

Flipping 1000 coins

flips <- rbinom(100000, 1000, .5)

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FOUNDATIONS OF PROBABILITY IN R

Flipping 1000 coins

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FOUNDATIONS OF PROBABILITY IN R

Normal distribution has mean and standard deviation

X ∼ Normal(μ,σ) σ = √ Var(X)

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FOUNDATIONS OF PROBABILITY IN R

Normal approximation to the binomial

binomial <- rbinom(100000, 1000, .5)

μ = size ⋅ p σ =

expected_value <- 1000 * .5 variance <- 1000 * .5 * (1 - .5) stdev <- sqrt(variance) normal <- rnorm(100000, expected_value, stdev)

√ size ⋅ p ⋅ (1 − p)

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FOUNDATIONS OF PROBABILITY IN R

Comparing histograms

compare_histograms(binomial, normal)

SLIDE 8

Let's practice!

FOU N DATION S OF P R OBABIL ITY IN R

SLIDE 9

The Poisson distribution

FOU N DATION S OF P R OBABIL ITY IN R

David Robinson

Chief Data Scientist, DataCamp

SLIDE 10

FOUNDATIONS OF PROBABILITY IN R

Flipping many coins, each with low probability

binomial <- rbinom(100000, 1000, 1 / 1000)

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FOUNDATIONS OF PROBABILITY IN R

Properties of the Poisson distribution

binomial <- rbinom(100000, 1000, 1 / 1000) poisson <- rpois(100000, 1) compare_histograms(binomial, poisson)

X ∼ Poisson(λ) E[X] = λ Var(X) = λ

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FOUNDATIONS OF PROBABILITY IN R

Poisson distribution

SLIDE 13

Let's practice!

FOU N DATION S OF P R OBABIL ITY IN R

SLIDE 14

The geometric distribution

FOU N DATION S OF P R OBABIL ITY IN R

David Robinson

Chief Data Scientist, DataCamp

SLIDE 15

FOUNDATIONS OF PROBABILITY IN R

Simulating waiting for heads

flips <- rbinom(100, 1, .1) flips # [1] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 # [16] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 which(flips == 1) # [1] 8 27 44 55 82 89 which(flips == 1)[1] # [1] 8

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FOUNDATIONS OF PROBABILITY IN R

Replicating simulations

which(rbinom(100, 1, .1) == 1)[1] # [1] 28 which(rbinom(100, 1, .1) == 1)[1] # [1] 4 which(rbinom(100, 1, .1) == 1)[1] # [1] 11 replicate(10, which(rbinom(100, 1, .1) == 1)[1]) # [1] 22 12 6 7 35 2 4 44 4 2

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FOUNDATIONS OF PROBABILITY IN R

Simulating with rgeom

geom <- rgeom(100000, .1) mean(geom) # [1] 9.04376

X ∼ Geom(p) E[X] = − 1 p 1

SLIDE 18

Let's practice!

FOU N DATION S OF P R OBABIL ITY IN R