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What is the range of this function?

Mathematics

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ivanzaharov [21]3 years ago

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Nezavi [6.7K]

$\mathbb E\left(\dfrac{X-\mu}{\sigma}\right)=\dfrac1\sigma\mathbb E(X)-\dfrac\mu\sigma=\dfrac{\mu-\mu}\sigma=0$

$\mathbb E\bigg(\left(\dfrac{X-\mu}\sigma\right)^2\bigg)=\dfrac1{\sigma^2}\mathbb E\left(X^2-2\mu X+\mu^2\right)=\dfrac{\mathbb E(X^2)-2\mu\mathbb E(X)+\mu^2}{\sigma^2}$
$=\dfrac{\mathbb E(X^2)-2\mu^2+\mu^2}{\sigma^2}=\dfrac{\mathbb E(X^2)-\mu^2}{\sigma^2}=\dfrac{\mathbb E(X^2)-\mathbb E(X)^2}{\sigma^2}$
$=\dfrac{\mathbb V(X)}{\sigma^2}=\dfrac{\sigma^2}{\sigma^2}=1$

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Step-by-step explanation:

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3 years ago

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ss7ja [257]

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Step-by-step explanation:

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What is the difference between the mean and the median of the data set?

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The answer is 1

Step-by-step explanation:

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22+8+10+18+12+20 = 90

90/6=15

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22,8,10,18, 12,20

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