These Ten-Year-Series (TYS) worked solutions with video explanations for 2022 A Level H2 Mathematics Paper 2 Question 8 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2022 A Level H2 Math Paper 2 Question 8
(a)
The independent random variables $X$ and $Y$ are such that $X\sim$$N\left( p,{{q}^{2}} \right)$ and $Y\sim$$N\left( s,{{t}^{2}} \right)$. Write down an expression for the distribution of the random variable $aX-bY$, where $a$ and $b$ are constants.
[2]
(a) The independent random variables $X$ and $Y$ are such that $X\sim$$N\left( p,{{q}^{2}} \right)$ and $Y\sim$$N\left( s,{{t}^{2}} \right)$. Write down an expression for the distribution of the random variable $aX-bY$, where $a$ and $b$ are constants.
[2]
(b)
The random variable $V$ is normally distributed with standard deviation $2$. The probability that $V>8$ is equal to the probability that $V<4$.
(b) The random variable $V$ is normally distributed with standard deviation $2$. The probability that $V>8$ is equal to the probability that $V<4$.
(i) Draw a sketch to show the distribution of $V$, including the main features of the curve.
[2]
(i) Draw a sketch to show the distribution of $V$, including the main features of the curve.
[2]
(ii) On your sketch, shade the area represented by $\text{P}\left( V>10 \right)$ and state its value.
[2]
(ii) On your sketch, shade the area represented by $\text{P}\left( V>10 \right)$ and state its value.
[2]
(c)
The random variable $W$ is such that $W\sim\text{B}\left( 8,p \right)$. The mean of $W$ is $1.2$ times the variance of $W$.
Find $\text{P}\left( W<2 \right)$.
[3]
(c) The random variable $W$ is such that $W\sim\text{B}\left( 8,p \right)$. The mean of $W$ is $1.2$ times the variance of $W$.
Find $\text{P}\left( W<2 \right)$.
[3]
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