A question in random variables and random processes

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SUMMARY

The discussion centers on the mathematical treatment of random variables, specifically focusing on the expectation of a function of a random variable. The key formula presented is E(f(A))=∫f(a)dF(a), where F(a) represents the cumulative distribution function of the random variable A. Participants emphasize the importance of understanding the relationship between random variables X and Y as functions of the phase. This foundational concept is crucial for further exploration in probability theory and stochastic processes.

PREREQUISITES
  • Understanding of random variables and their properties
  • Familiarity with probability distribution functions
  • Basic knowledge of calculus, particularly integration
  • Concept of expectation in probability theory
NEXT STEPS
  • Study the properties of cumulative distribution functions (CDFs)
  • Explore the concept of expectation in more depth, including conditional expectation
  • Learn about stochastic processes and their applications
  • Investigate advanced topics in probability theory, such as moment generating functions
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Students and professionals in mathematics, statistics, and engineering, particularly those focusing on probability theory and stochastic processes.

Shloa4
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I will be grateful for some help here.
Thanks :smile:
 

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The phase is the random variable of interest. X and Y are functions of the phase.
The basic idea is that if A is a random variable and f a function of A, then
E(f(A))=∫f(a)dF(a), where F(a) = P(A≤a), the distribution function for A.
 

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