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function whoseon { who > $temp kdialog --textbox $temp 500 10 } function memusage { cat /proc/meminfo > $temp kdialog --textbox $temp 300 500 } while [ 1 ] do kdialog --menu "Sys Admin Menu" "1" "Display disk space" "2" "Display users" "3" "Display memory usage" "0" "Exit" > $temp2 if [ $ -eq 1 ] then break fi selection=`cat $temp2` case $selection in 1) diskspace ;; 2) whoseon ;; 3) memusage ;; 0) break ;; *) kdialog --msgbox "Sorry, invalid selection" esac done $

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Let ( , F , P ) be a probability space and (Y , ) be a measurable space Then a random variable is formally de ned as a measurable function : Y In other words, the preimage of the well-behaved subsets of Y (the elements of ) are events, and hence are assigned a probability by P When the measurable space is the measurable space over the real numbers, one speaks of real-valued random variables Then, the function is a real-valued random variable if { | ( ) u r} F , r R (A14)

The probability distribution of a real-valued variable can be uniquely described by its cumulative distribution function F (x) (also called a distribution function), which is de ned by F (x) = P ( u x) (A15)

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for any x in R More generally, given a random variable : Y between a probability space ( , F , P ), the sample space, and a measurable space (Y , ), called the state space, a probability distribution on (Y , ) is a probability measure P : [0, 1] on the state space, where P is the push-forward measure of P A distribution is called discrete if its cumulative distribution function consists of a sequence of nite jumps, which means that it belongs to a discrete random variable , a variable which can only attain values from a certain nite or countable set Discrete distributions are characterized by a probability mass function p such that P ( = x) = p(x) A distribution is called continuous if its cumulative distribution function is continuous A random variable is called continuous if its distribution function is continuous In that case P ( = x) = 0 for all x R Note also that there are probability distribution functions which are neither discrete nor continuous

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