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Let X be a random variable such that P(X = 1) = 0.4 and P(X =...

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Let X be a random variable such that P(X = 1)= 0.4 and P(X = 0) = 0.6.Â Â ComputeVar(X).

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3.7 Ratings (438 Votes)

xÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â pÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â xpÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â x²p

1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4

0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0

---------------------------------------------------------------------------------------------

TotalÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4

So,

E(X) = 0.4

Var(X) = E(X²) - (E(X))²

Â Â Â Â Â Â Â = 0.4 - 0.4² = 0.24

So,

Answer is:

0.24

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