Find the variance in uniform distribution if X is uniformly distributed over…

Variance Formula Recap
For a continuous uniform distribution over the interval (a, b), the formula is:

Variance = ((b - a)²) / 12

Step-by-Step Calculation
Identify the parameters: Here, a = 5 and b = 30.

Calculate the range: b - a = 30 - 5 = 25.

Square the range: 25² = 625.

Divide by 12: 625 / 12 ≈ 52.083.

Why this is a Continuous Distribution
The distribution is continuous because the variable can take on any real number within the interval (5, 30). Because there are infinitely many values between 5 and 30, we use a Probability Density Function (PDF) to represent it, which is represented by a horizontal line over the interval on a graph.

Comparison with Discrete Uniform Distribution
If the question asked about a discrete uniform distribution (like selecting a random whole number from 5 to 30), the formula would change to:

Variance = ((n² - 1) / 12)

Where 'n' is the number of possible outcomes. In that scenario, the variance would be calculated very differently because you are dealing with distinct, countable points rather than a continuous range.