Find out the answer to "Is E(X2) equal to (E(X))2?"

rocedwrp

Answered question

2021-09-18

E (X^{2})

equal to

{(E (X))}^{2}

Answer & Explanation

Latisha Oneil

Skilled2021-09-19Added 100 answers

The expected value is the sum of the product of each possibility x with its probability (X=x), or as the formula suggests:

E (X) = \sum x P (X = x)

Apply each of the suggested options to the formula

{(E (X))}^{2} = {(\sum x P (X = x))}^{2}

= (\sum x P (X = x)) (\sum x P (X = x))

E (X^{2}) = \sum x^{2} P (X = x)

\sum x^{2} P (X = x) \neq (\sum x P (X = x)) (\sum x P (X = x))

Therefore,

E (X^{2}) \neq {(E (X))}^{2}

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