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[Maximum number: 3]

The random variable X has probability distribution $\operatorname{Po}(8)$ .

(a)

$\bar{X}$ denotes the sample mean of n>1 independent observations from X.

[ 3 ]

(i)

Write down $\mathrm{E}(\bar{X})$ and $\operatorname{Var}(\bar{X})$ .

[ 2 ]

$\quad \mathrm{E}(\bar{X})=8$

A1
$\operatorname{Var}(\bar{X})=\frac{8}{n}$

(ii)

Hence, give a reason why $\bar{X}$ is not a Poisson distribution.

[ 1 ]

$\quad \mathrm{E}(\bar{X}) \neq \operatorname{Var}(\bar{X})($ for n>1)
Note: Only award the R1 if the two expressions in (b)(i) are different.

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