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To determine the mean and variance of two intervals, follow these steps:
For example, consider the intervals [0, 5) and [10, 15). The midpoints are 2.5 and 12.5, respectively. The interval lengths are both 5, so the total length is 10. The weighted mean is (2.5 * 5 + 12.5 * 5) / 10 = 7.5. The midpoint variances are [(5 - 0)^2 / 12] and [(15 - 10)^2 / 12], respectively. The interval length squares are both 25, so the total length squared is 50. The weighted variance is [(25 * 1/12 * ((5-0)^2/12)) + (25 * 1/12 * ((15-10)^2/12))] / 50 - 7.5^2 = 8.75. Therefore, the mean and variance of the two intervals are 7.5 and 8.75, respectively.