Triangular Distribution

• cdf
  
  $$f(x) = \left\{ \begin{array}{ll} x & 0 \le x \le 1 \\ 2 - x & 1 < x \le 2 \\ 0 & otherwise \end{array} \right.$$
  
  
  Its curve is shown on page 328

• Steps

  Step 1.

  cdf
  

  $$F(x) = \left\{ \begin{array}{ll} 0 & x \le 0 \\ \frac{x^2}... ...{(2-x)^2}{2} & 1 < x \le 2 \\ 1 & x > 2 \end{array} \right.$$

  
  

  Step 2.

  let $R = \frac{X^2}{2} ~~ {\rm for}~~ 0 < X \le 1$ and $R = 1 - \frac{(2-x)^2}{2} ~~{\rm for}~~ 1 < x \le 2$

  Step 3.

  Solve $X$ in terms of $R$

  
  

  $$X = \left\{ \begin{array}{ll} \sqrt{2R} & 0 \le R \le \frac{... ...2 - \sqrt{2(1-R)} & \frac{1}{2} < R \le 1 \end{array} \right.$$