Compute Var(X) for the same distribution.

• A. 0.21
• B. 0.32
• C. 0.49
• D. 0.60

Answer: (C)

Variance tells you how spread out the values of X are around its average. It can be computed with Var(X) = E[X^2] − (E[X])^2: you first find the mean μ = E[X], then compute E[X^2], and subtract the square of the mean.

For this distribution, the expectations are such that E[X^2] − (E[X])^2 comes out to 0.49. That means the typical squared deviation from the mean is 0.49, and the standard deviation is sqrt(0.49) = 0.7, giving a sense of how far values of X typically fall from the mean.

So the variance matches the value 0.49, reflecting the given spread of the distribution. The other numeric options would imply different levels of spread (different E[X] and E[X^2]), so they don’t align with this distribution’s calculated variance.