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  4. If μ is the mean of distribution yi, fi then ∑ fi (yi - μ) is equal to

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Q. If $\mu$ is the mean of distribution $\{y_i, f_i\}$, then $\sum f_i (y_i - \mu)$ is equal to

Statistics

Solution:

$\sum f_{i}\left(y_{i} - \mu\right) = \sum\left(f_{i} y_{i} - f_{i}\mu\right) = \sum f_{i} y_{i} - \mu\sum f_{i} $
$=\sum f_{i}y_{i } - \left(\frac{\sum f_{i}y_{i}}{\sum f_{i}}\right) \sum f_{i} = 0 $