Claim:Random variables satisfy distributivity

From CS2800 wiki
If [math]X [/math], [math]Y [/math], and [math]Z [/math] are random variables on a probability measure [math](\href{/cs2800/wiki/index.php/S}{S},\href{/cs2800/wiki/index.php/Pr}{Pr}) [/math], then [math]X(Y + Z) = XY + XZ [/math].