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Random variables as functions We consider in this chapter real random variables (ie, realvalued random variables) In the chapter on Random Vectors and Joint Distributions, we extend the notion to vectorvalued random quantitesThe fundamental idea of a real random variable is the assignment of a real number to each elementary outcome $\omega$ in the basic space $\Omega$. È ¢ B ± Ì _ Å Í ¯ ¶ ñ ¾ ê Ì § Æ ¢ Á Ä à à É ¡ I Î í Æ µ Ä t X ê n Z ¯ ð ø ¦ é J i _ È Ç Æ Í Ù È Á ½ ó µ É é B Ü ½ A x V ¤ a Ì ¾ ê @ É Í u Ð ï ¶.