Multiplying random value by variance + motivation

However, it appears that this is only necessary if the random variable starts out as standard normal. In summary, to obtain a normally distributed random variable with the desired variance, you can multiply the original value by the standard deviation (square root of variance). This rule also applies to other distributions, resulting in a random variable with the same distribution.
  • #1
JamesGoh
143
0
Just a quick question.

If you want any value to follow a particular probability distribution function (pdf), do you have to multiply that value by the variance of the desired pdf ?
 
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  • #2
JamesGoh said:
Just a quick question.

If you want any value to follow a particular probability distribution function (pdf), do you have to multiply that value by the variance of the desired pdf ?

What is the probability distribution of the given random variable? If it starts out as standard normal, you can multiply it by the standard deviation (square root of variance) to get a normally distributed r.v. with the desired variance. In general by multiplying by the s.d. you will get a r.v. with the same kind of distribution.
 
  • #3
thanks for that

Initially, I was concerned with a value following any pdf distribution being multiplied by a specific pdf variance
 

1. What is the purpose of multiplying a random value by variance?

The purpose of multiplying a random value by variance is to introduce variability into a data set. This is commonly used in statistical analysis and simulations to create a more realistic representation of a population or system.

2. How does multiplying a random value by variance affect the data?

Multiplying a random value by variance increases the spread of the data. This means that the data points will have a wider range of values, making it more representative of a real-life scenario.

3. What is the role of motivation in this equation?

Motivation is often used as a multiplier in this equation to represent the influence of external factors on the data. It can be used to simulate the impact of different variables or to model the effect of human behavior on a system.

4. Can multiplying a random value by variance + motivation be applied to all types of data?

Yes, this equation can be applied to various types of data, including numerical, categorical, and even qualitative data. However, the interpretation and application may differ depending on the type of data being analyzed.

5. How do scientists determine the appropriate values for variance and motivation in this equation?

The values for variance and motivation are typically determined through research and experimentation. Scientists may use statistical methods or previous data to estimate the appropriate values that will best represent the real-world scenario they are trying to simulate.

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