The independent random variables $X$ and $Y$ are such that $X\sim$ $N\left( p,{{q}^{2}} \right)$ and

Question

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] The random variable $V$ is normally distributed with standard deviation $2$. The probability that $V>8$ is equal to the probability that $VDraw a sketch to show the distribution of $V$, including the main features of the curve. [2] On your sketch, shade the area represented by $\mathrm{P}\left( V>10 \right)$ and state its value. [2] The random variable $W$ is such that $W\sim\mathrm{B}\left( 8,p \right)$. The mean of $W$ is $1.2$ times the variance of $W$. Find $\mathrm{P}\left( W[3]

Accepted Answer

(a) $\mathrm{N}(ap-bs, a^2q^2+b^2t^2)$ (b)(i) $\mathrm{N}(6, 4)$ (b)(ii) $0.0228$ (c) $0.605$

N2022 P2 Q8

N2022 P2 Q8

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