Given that the random variables $X$ and $Y$ have distributions $N(60, 25)$ and $N(54, 64)$ respectiv

Question

Given that the random variables $X$ and $Y$ have distributions $N(60, 25)$ and $N(54, 64)$ respectively, and that $\bar{X}$ and $\bar{Y}$ denotes the means of $7$ independent observations of $X$ and $11$ independent observations of $Y$ respectively. State the sampling distributions of $\bar{X}-\bar{Y}$ $2\bar{X}+5\bar{Y}$ $\frac{{{X}{1}}+{{X}{2}}+{{X}{3}}-{{Y}{1}}-{{Y}{2}}-…-{{Y}{5}}}{8}$

Accepted Answer

(i) $\bar{X} - \bar{Y} \sim N(6, 9.39)$; (ii) $W \sim N(390, 160)$; (iii) $Q \sim N(-11.25, 6.17)$

Worked Example 2

Worked Example 2

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