Mean, mode and median can all be used to give an average value, but each can be considered more appropriate in different situations. Give an example for each measure where it is the most appropriate average value and explain why it is the most appropriate measure to use. 3 marks

What is a scatter plot?

c) Find the Yule-Walker equation for the \( \mathrm{AR}(2) \) process \[ X_{t}=\frac{1}{3} X_{t-1}+\frac{2}{9} X_{t-2}+e_{t}, e_{t} \sim W N\left(0, \sigma_{e}^{2}\right) \]

Define un diagrama de dispersión y describe su propósito en la estadística.

If \( n(A)=8 \) and \( n(A \cap B)=2 \), then \( n\left[(A \cap B)^{\prime} \cap A\right] \) is equal to \( \begin{array}{ll}\text { (a) } 2 & \text { (b) } 4 \\ \text { (c) } 6 & \text { (d) } 8 \\ \text { (e) } 10 & \end{array} \)

here are 100 students in a class. In an examination, 50 of them ailed in Mathematics, 45 failed in Physics, 40 failed in Biology nd 32 failed in exactly two of three subjects. Only one studen assed in all the subjects. Then the number of students failing all the three subjects a) Is 12 a) Is 4 t) Is 2 d) Cannot be determined from the given information