Difference between revisions of "Eleisha's Segment 17: The Towne Family - Again"

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3. What is its cumulative distribution function (CDF)?
 
3. What is its cumulative distribution function (CDF)?
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CDF = F(x)
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<math> F(x) = x(1-\frac{x}{4}) \text{ for } 0<x<2 \text{, 0 otherwise } </math>
  
 
[[File:Eleisha_Feb_24_CDF.png]]
 
[[File:Eleisha_Feb_24_CDF.png]]

Revision as of 16:30, 24 February 2014

Class Activity

1. Sketch the distribution Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_X(x)}

Eleisha Feb 24 PDF.png

2. What is the distribution's mean and standard deviation? Mean:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Mean} = E(x) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E(x) = \int_0^2 xp(x) dx = \int_0^2 x\left(1 - \frac{x}{2}\right) dx = \frac{x^2}{2} - \frac{x^3}{6} \Big|_0^2 = \frac{2}{3}}

Standard Deviation:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Standard Deviation} = \sqrt{\text{Variance}} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Variance} = \int_0^2 x^2p(x) dx - [E(x)]^2 = \left(\frac{x^3}{3} - \frac{x^4}{8}\right)\Big|_0^2 - [E(x)]^2 = \frac{6}{9} -\frac{4}{9} = \frac{2}{9} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{\frac{2}{9}}}

3. What is its cumulative distribution function (CDF)?

CDF = F(x)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x) = x(1-\frac{x}{4}) \text{ for } 0<x<2 \text{, 0 otherwise } }

Eleisha Feb 24 CDF.png