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.

Answer 1

No, they are not

Explanation:

No, they are not . The probability distribution could have the same mean value , but the values of the sample space that are further could be more probable , yet the mean stay the same ( for example if the probability distribution is symmetric).

Recalling the relationship between expected value and standard deviation of a random variable X

σ²(X)=E(X²) - (E(X))²

then E(X) could be the same , but E(X²) would be different if the probability distribution is more dispersed