Distribution of minimum of random variables

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SUMMARY

The discussion focuses on the joint distribution function of two independent random variables, X and Y, specifically for U=min(X,Y) and V=max(X,Y). The initial confusion was clarified when it was established that X and Y are independent random variables, simplifying the derivation of the marginal distributions for U and V. The participant initially proposed a joint distribution expression of 2[u(v-u) + ½u^2], which indicates an understanding of the relationship between the minimum and maximum of the random variables.

PREREQUISITES
  • Understanding of joint distribution functions
  • Knowledge of independent random variables
  • Familiarity with minimum and maximum functions in probability
  • Basic concepts of marginal distributions
NEXT STEPS
  • Study the properties of joint distribution functions for independent random variables
  • Learn how to derive marginal distributions from joint distributions
  • Explore the concept of order statistics in probability theory
  • Investigate applications of minimum and maximum distributions in statistical analysis
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Statisticians, data scientists, and students studying probability theory who are interested in understanding the distribution of minimum and maximum values of random variables.

Millie
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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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:redface:

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

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