Question

Determine the cumulative distribution function for following:(2 Marks) F(x) 0 x < 0 0.2 x 0 <= x < 4 0.04 x + 0.64 4 <= x < 9 1 9 <= x

Answer 1

The cumulative distribution function

$$F(x)= \begin{cases} 0 &x<0 \\ 0.2x &0\le x<4\\ 0.04x+0.64 & 4\le x<9\\ 1& x\ge9\\ \end{cases}$$

Determine the probability density function

$$f(x)= \begin{cases} 0 &x<0 \\ 0.2 &0\le x<4\\ 0.04 & 4\le x<9\\ \end{cases}$$