Composite Discrete Random Experiment

See: Compound Random Variable, Compound Discrete Random Experiment.

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References

2015

• (Mestrovic, 2015) ⇒ (2015). "On Some Compound Random Variables Motivated by Bulk Queues". In: Mathematical Problems in Engineering, 2015.
  • QUOTE: Let $X_1, X_2, \cdots$, be a sequence of mutually independent and identically distributed positive random variables that are independent of the nonnegative integer-valued random variable $Y$. Then the random variable $S_Y$ defined as a sum

[math]\displaystyle{ S_Y=X_1+X_2+\cdots+X_Y }[/math]

(1)

 :: is called a compound random variable (or a compound distribution). In this respect, the distribution of $Y$ is a compounded random variable (or a compounded distribution), while the random variable $X$ is called a compounding random variable (or a compounding distribution).

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