The mean and standard deviation of a random variable X are $10$ and $5$ respectively. Find.
$E ({(\frac{x - 10}{5})}^{2})$ .

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Solution

$E (X) = 10$

We know that $E (\frac{x - 10}{5}) = E (\frac{x}{5} - 2)$

$= \frac{E (X)}{5} - 2$

$= \frac{10}{5} - 2$

$= 0$

Standard deviation is $σ = 5$

$E ({(\frac{x - 10}{5})}^{2}) - {[E (\frac{x - 10}{5})]}^{2} = σ^{2}$

$⟹ E ({(\frac{x - 10}{5})}^{2}) = 25$

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The mean and standard deviation of a random variable X are 10 and 5 respectively. Find.E((x−105)2).

E(X)=10We know that E(x−105)=E(x5−2)=E(X)5−2=105−2=0Standard deviation is σ=5E((x−105)2)−[E(x−105)]2=σ2⟹E((x−105)2)=25

The mean and standard deviation of a random variable X are $10$ and $5$ respectively. Find.
$E ({(\frac{x - 10}{5})}^{2})$ .

$E (X) = 10$

We know that $E (\frac{x - 10}{5}) = E (\frac{x}{5} - 2)$

$= \frac{E (X)}{5} - 2$

$= \frac{10}{5} - 2$

$= 0$

Standard deviation is $σ = 5$

$E ({(\frac{x - 10}{5})}^{2}) - {[E (\frac{x - 10}{5})]}^{2} = σ^{2}$

$⟹ E ({(\frac{x - 10}{5})}^{2}) = 25$