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.

No, they are not

Step-by-step 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