6. A continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} a x - b x ^ { 2 } & 0 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
Given that the mode is 1
- show that \(a = 2 b\)
- Find the value of \(a\) and the value of \(b\)
- Calculate F(1.5)
- State whether the upper quartile of \(X\) is greater than 1.5, equal to 1.5, or less than 1.5 Give a reason for your answer.