To calculate the standard deviation when the variance of a probability distribution is given as 2, follow this correct procedure:

• The standard deviation is the square root of the variance. This is because variance measures the average squared deviation from the mean, while standard deviation measures the average deviation in the original units of the data

• Given the variance σ2=2\sigma^2=2σ2=2, calculate the standard deviation σ\sigma σ as:

σ=2≈1.414\sigma =\sqrt{2}\approx 1.414σ=2​≈1.414

Thus, the standard deviation is approximately 1.414.

Summary of the procedure:

1. Identify the variance of the probability distribution (here, 2).
2. Take the square root of the variance.
3. The result is the standard deviation.

This method applies directly whether the variance is for a population or a probability distribution