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If I have: - Standard deviation - Skew

  1. What additional information can I calculate ?
  2. Could I calculate Expected Value?
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No.

For instance, consider a Normal distribution having standard deviation of 1. It has a skewness of 0. Its mean, i.e., expected value, can be anything.

Edit: In response to edited question.

My answer "No" above refers to whether you can compute the expected value.

If you know the standard deviation, you know something about how spread out the distribution is. For instance, if the standard deviation is zero, then the distribution takes a particular value with probability one, i.e., is essentially deterministic (aside from a set of probability zero), but that value could be anything.

If you know the skewness, you know something about how symmetric or not the distribution is, but not completely. For instance, a symmetric distribution has a skewness of zero, but an asymmetric distribution can potentially have a skewness of zero as well.

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