Question

Consider two discrete probability distributions with the same sample space and the

same expected value. Are the standard deviations of the two distributions necessarily equal? Explain. 

Yes, because both distributions have the same sample space, they will have the same standard deviation as well.

No, the standard deviations of two different discrete probability distributions are never equal.

Yes, because both distributions have the same expected value, they will have the same standard deviation as well.

No, the individual probabilities may differ in a way that produces the same expected value but a different standard deviation.

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