These Ten-Year-Series (TYS) worked solutions with video explanations for 1978 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
A fair die is thrown once and random variable $X$ denotes the score obtained. Write down $\text{E}\left( X \right)$ and show that $\text{Var}\left( X \right)=\frac{35}{12}$. The die is thrown twice, and ${{X}_{1}}$and${{X}_{2}}$ obtained from each attempt.
Tabulate the probability distribution of $Y=\left| {{X}_{1}}-{{X}_{2}} \right|$, and find $E\left( Y \right)$.
The random variable $Z$ is defined by $Z={{X}_{1}}-{{X}_{2}}$. State with reasons whether or not
(i)
$E\left( {{Z}^{2}} \right)=E\left( {{Y}^{2}} \right)$.
(i) $E\left( {{Z}^{2}} \right)=E\left( {{Y}^{2}} \right)$.
(ii)
$\text{Var}\left( Z \right)=\text{Var}\left( Y \right)$.
(ii) $\text{Var}\left( Z \right)=\text{Var}\left( Y \right)$.
Share with your friends!
