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Standard XII

Mathematics

Probability Distribution

The mean and ...

Question

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

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Solution

$M e a n = E (X) = 10$

standard deviation $= σ = 5$

We know that

$σ^{2} = E (X^{2}) - (E (X))^{2}$

$⟹ 5^{2} = E (X^{2}) - 10^{2}$

$⟹ E (X^{2}) = 125$

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The mean and standard deviation of a random variable X are 10 and 5 respectively. Find E(X2)

Mean=E(X)=10standard deviation=σ=5We know thatσ2=E(X2)−(E(X))2⟹52=E(X2)−102⟹E(X2)=125

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

$M e a n = E (X) = 10$

standard deviation $= σ = 5$

We know that

$σ^{2} = E (X^{2}) - (E (X))^{2}$

$⟹ 5^{2} = E (X^{2}) - 10^{2}$

$⟹ E (X^{2}) = 125$