8. The formula of variance of uniform or rectangular distribution is as 
    a) ((b - a) ^ 2) / 6 
    b) ((b + a) ^ 2) / 12 
    c) ((b - a) ^ 3) / 8 
    d) ((b + a) ^ 2) / 2

The variance of a uniform (or rectangular) distribution, denoted \( U(a, b) \), where \( a \) and \( b \) are the minimum and maximum values respectively, is given by:

\[
\text{Var}(X) = \frac{(b - a)^2}{12}
\]

Therefore, the correct answer is:

a) \(\frac{(b - a)^2}{12}\)

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How do you derive the variance formula for a uniform distribution?
2. What is the mean of a uniform distribution \( U(a, b) \)?
3. How would the variance change if the distribution was not uniform but normal with the same \( a \) and \( b \)?
4. Can you provide an example calculation of variance for a uniform distribution with specific values of \( a \) and \( b \)?
5. How is the uniform distribution used in practical applications?

**Tip:** For any continuous uniform distribution, the variance formula \(\frac{(b - a)^2}{12}\) can help you quickly determine the spread of the distribution, which is useful in many statistical analyses and simulations.

Explore how to calculate the variance of a uniform distribution using the formula Var(X) = ((b - a)^2) / 12. This formula is crucial in probability and statistics, helping determine the spread of values in uniform distributions. Ideal for undergraduate students and anyone interested in statistical analysis.

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