Mean and Variance Question

abc4616

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Sep 30, 2006
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If a random variable X is defined such that E[(X-1)^2]=10 and E[(X-2)^2]=6, find the mean and variance of X.

Does anyone know how to approach this question??
 
Using the additive and homogeneous properties we get:
\(\displaystyle \begin{array}{rcl}
E\left[ {\left( {X - 1} \right)^2 } \right] = 10\quad & \Rightarrow & \quad E\left( {X^2 } \right) - 2E(X) + 1 = 10 \\
E\left[ {\left( {X - 2} \right)^2 } \right] = 6\quad & \Rightarrow & \quad E\left( {X^2 } \right) - 4E(X) + 4 = 6 \\ \end{array}.\)

Solve the system for E(X2)&E(X).\displaystyle E\left( {X^2 } \right)\quad \& \quad E\left( X \right).

Recall that V(X)=E(X2)E2(X).\displaystyle V(X) = E\left( {X^2 } \right) - E^2 \left( X \right).
 
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