Eleisha's Segment 17: The Towne Family - Again

Class Activity

1. Sketch the distribution $p_{X}(x)$

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

${\text{Mean}}=E(x)$

$E(x)=\int _{0}^{2}xp(x)dx=\int _{0}^{2}x\left(1-{\frac {x}{2}}\right)dx={\frac {x^{2}}{2}}-{\frac {x^{3}}{6}}{\Big |}_{0}^{2}={\frac {2}{3}}$

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