Understanding Probability Distributions for Generating Random Data

In summary, to generate 40% of a set of 50 items 60% of the time, you can use the Pareto Distribution's pdf to create duplicate items until you reach the desired proportion, and then use a uniform rule to select from the set.
  • #1
EliteLegend
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I have recently come across the 80/20 rule... I am using the Pareto Distribution's pdf to generate some dataset that I wanted... Now if I have a set of 50 items and I need to generate 40% of these items 60% of the times, how am I supposed to go about doing this? I know how to select items with certain probabilities but this task is confusing me... Anyone has some inputs for me please?
 
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  • #2
One way is to create duplicate (multiplicate) items until you reach the desired proportion, then use a uniform rule to select.

For example, if I had 2 items {x, y} and wanted to obtain x 67% of the time, I'd duplicate x once, and make draws from the set {x, x, y}.
 
  • #3
To select one of m items, from a total of n items, a proportion y of the time, you need to select each of the m items with probability y/m, and each of the remaining n-m items with probability (1-y)/(n-m)
 
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1. What is a random number?

A random number is a number that is generated without any predictable pattern or bias. It is used in various fields such as statistics, gambling, and cryptography to introduce an element of chance.

2. How are random numbers generated?

Random numbers can be generated through various methods such as using physical objects like dice or coins, mathematical algorithms, or computer programs. The method used depends on the application and the level of randomness required.

3. Are random numbers truly random?

No, random numbers generated by a computer or mathematical algorithm are not truly random. They are pseudo-random, meaning they follow a predetermined sequence that appears random but can be replicated if the algorithm is known.

4. Can random numbers be predicted?

It is highly unlikely for truly random numbers to be predicted, but pseudo-random numbers can be predicted if the algorithm used to generate them is known. This is why it is important to use high-quality random number generators for applications that require true randomness.

5. What is the significance of random numbers in science?

Random numbers are essential in science for conducting experiments, simulations, and statistical analyses. They help to eliminate bias and introduce an element of chance, making the results more accurate and reliable. They are also used in cryptography to ensure secure communication and data protection.

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