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Anna Karlin Most Slides by Alex Tsun
Anna Karlin Most Slides by Alex Tsun Poisson RV Example The Zoo of - - PowerPoint PPT Presentation
Anna Karlin Most Slides by Alex Tsun Poisson RV Example The Zoo of - - PowerPoint PPT Presentation
Anna Karlin Most Slides by Alex Tsun Poisson RV Example The Zoo of Discrete RVs The Negative Binomial RV The Bernoulli RV The Hypergeometric RV The Binomial RV probability students The Geometric RV Definition of The
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The Zoo of Discrete RV’s
probability students Definition of Expectation
- The Bernoulli RV
- The Binomial RV
- The Geometric RV
- The Uniform RV
- The Poisson RV
- The Negative Binomial RV
- The Hypergeometric RV
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random variables
Important Examples: Uniform(a,b): Bernoulli(p): P(X = 1) = p, P(X = 0) = 1-p μ = p, σ2= p(1-p) Binomial(n,p) μ = np, σ2 = np(1-p) Poisson(λ): μ = λ, σ2 = λ Bin(n,p) ≈ Poi(λ) where λ = np fixed, n →∞ (and so p=λ/n → 0) Geometric(p) P(X = k) = (1-p)k-1p μ = 1/p, σ2 = (1-p)/p2
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Probability
4.1 Continuous random Variables Basics
Anna Karlin Most Slides by Alex Tsun
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Agenda
- Probability Density Functions (PDFs)
- Cumulative Distribution Functions (CDFs)
- From Discrete to Continuous
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CDF Intuition
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PDF Intuition
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PDF Intuition
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Probability Density Functions (PDFs)
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Random Picture
probability students Definition of Expectation
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CDF Intuition
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CDF Intuition
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CDF Intuition
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CDF Intuition
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CDF Intuition
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CDF Intuition
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CDF Intuition
1 1
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CDF Intuition
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CDF Intuition
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CDF Intuition
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Cumulative Distribution Functions (CDFs)
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From Discrete to Continuous
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Probability
4.2 Zoo of Continuous RVs
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Agenda
- The (Continuous) Uniform RV
- The Exponential RV
- Memorylessness
SLIDE 39 pdf
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The Uniform (Continuous) RV
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