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You are here: Home Stats Department Introduction to probability - IN TRANSLATION Samdreifingar Hjálparsetning um samdreifni

Hjálparsetning um samdreifni

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Hjálparsetning: Ef $ X$ og $ Y$ eru óháðar hendingar, þá er $ E[X\cdot Y]=E[X] \cdot E[Y]$ .

$ p(x,y)=p_X(x)\cdot
p_Y(y)$ .


$\displaystyle E[X\cdot Y]$ $\displaystyle =$ $\displaystyle \sum_x \sum_y x \cdot y \cdot p(x,y)$  
  $\displaystyle =$ $\displaystyle \sum_x \sum_y x \cdot y \cdot p_X(x)p_Y(y)$  
  $\displaystyle =$ $\displaystyle \left \{ \sum_x x \cdot p_X(x) \right \} \left \{ \sum_y \cdot y p_Y(y) \right \}$  
  $\displaystyle =$ $\displaystyle E[X] \cdot E[Y]$  






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