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

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Standard Deviation:
 
Standard Deviation:
  
<math> \text{Standard Deviation} = \sqrt{Variance} </math>
+
<math> \text{Standard Deviation} = \sqrt{\text{Variance}} </math>
 
 
<math>\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) =  </math>
 
  
 +
<math>\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} </math>
  
 +
<math> \text{Standard Deviation} = \sqrt{\text{Variance}}  = \sqrt{\frac{2}{9}}</math>
  
 
3. What is its cumulative distribution function (CDF)?
 
3. What is its cumulative distribution function (CDF)?

Revision as of 16:23, 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)}

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)?