Which of the following is a random variable? population size population mean sample size sample mean

9) At which value of x the function \( f(x)=(x-2)(x-3)^{2} \) has a local \( \begin{array}{lllll}\text { maximum? } & \text { (A) } \frac{-7}{3} & \text { (B) } \frac{-5}{2} & \text { (C) }-3 & \text { (D) } \frac{7}{3}\end{array} \)

(c) \( x^{4 / 3}=-64 \) \( x=\square \) (d) \( x^{3 / 2}=_{=} \) \( x=\square \) (e) \( x^{3 / 4}=-16 \) \( x=\square \)

\begin{tabular}{|l|l|}\hline I am thinking of the number 24. \\ What is half of \( 24 ? \)\end{tabular}

Solve the equation \( 5 x^{2}-6 x-3=0 \). Show all your working and give your answers correct to 2 decimal places.

State any two commonly used software tools for Time Series Analysis. (2Marks) Give an expression for \( X_{t}-5 X_{t-1}+7 X_{t-2}-3 X_{t-3} \quad \) in terms of second order di fferences.