Distribution of minimum of random variables

In summary, the distribution of the minimum of two independent random variables, also known as the minimum value distribution, is determined by the individual distributions of the two random variables. It can be calculated by finding the minimum value of each random variable and using mathematical formulas or statistical software programs. This distribution is significant in various statistical applications and can be skewed if the two random variables are not independent. The distribution of the minimum of random variables differs from the maximum value distribution in that it looks at the minimum values instead of the maximum values, and has different mathematical formulas and statistical properties.
  • #1
Millie
4
0
anyone's help would be really appreciated. I can't figure out that one.

If X and Y are joint random variables, what is the joint distribution funtion of U=min(X,Y) and V=max(X,Y).

I got something like 2[u(v-u) + ½u^2)]

then how do i worked towards and expression for the marginal distribution of U and V?
 
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  • #2
:redface:

sorry my mistake.. they are independent rv... now the question is quite simple! thanks anyway! :blushing:
 
  • #3
Anytime! :smile:
 

FAQ: Distribution of minimum of random variables

What is the distribution of the minimum of two independent random variables?

The distribution of the minimum of two independent random variables is also known as the minimum value distribution. This distribution is a type of order statistics distribution and is determined by the individual distributions of the two random variables. The minimum value distribution is often used in reliability and survival analysis.

How is the distribution of the minimum of random variables calculated?

The distribution of the minimum of random variables can be calculated by taking the minimum value of each random variable and then finding the distribution of those minimum values. This can be done through mathematical formulas or by using statistical software programs.

What is the significance of the distribution of the minimum of random variables?

The distribution of the minimum of random variables is important in many statistical applications, such as in risk analysis, reliability, and quality control. It provides information about the minimum possible value that can be observed from a set of random variables, and can help in making decisions and predictions based on these variables.

Can the distribution of the minimum of random variables be skewed?

Yes, the distribution of the minimum of random variables can be skewed. This can occur if one of the random variables has a skewed distribution or if the two random variables are not independent. In such cases, the minimum value distribution may not follow a normal distribution and may require special analysis techniques.

How does the distribution of the minimum of random variables differ from the maximum value distribution?

The distribution of the minimum of random variables is the opposite of the maximum value distribution. While the minimum value distribution looks at the minimum values of two or more random variables, the maximum value distribution looks at the maximum values. Additionally, the mathematical formulas and statistical properties of these two distributions are different.

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