1

To determine the mean and variance of two intervals, follow these steps:

- Find the midpoint of each interval by adding the lower and upper bounds of each interval and dividing by two.
- Calculate the weighted mean of the midpoints by multiplying each midpoint by its respective interval length, adding the products, and dividing by the total length of the two intervals.
- Calculate the weighted variance of the midpoints by adding the product of each interval length squared and its respective midpoint variance, dividing by the total length squared, and subtracting the squared weighted mean.

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.

Please start posting anonymously - your entry will be published after you log in or create a new account. This space is reserved only for answers. If you would like to engage in a discussion, please instead post a comment under the question or an answer that you would like to discuss

Asked: ** 2023-07-21 18:25:55 +0000 **

Seen: **20 times**

Last updated: **Jul 21 '23**

What is the method to achieve uneven tick intervals on the Y-axis?

What is the method for determining the variance between rows in Excel?

What is the process for calculating percentiles within specific time intervals?

What is the method for altering the color of the input text in a TextFormField in Flutter?

What is the procedure for utilizing the node-rdpjs library?

What is the method to change a PDF file to an Excel file using C#?

What is the method to make a TextButton inactive when the text field has no text?

What is the method to alter the background image in HTML?

What is the method for saving an entity with @EmbeddedId as its primary key in Hibernate?

Copyright QStack.ai, 2010-2023. Content on this site is licensed under the Creative Commons Attribution Share Alike 3.0 license.