Chapter-1 Note Blank-Part -2.pdf - Random Variables Idea You can think of a random variable as a numerical measurement assigned to each outcome of a

Chapter-1 Note Blank-Part -2.pdf - Random Variables Idea...

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Random Variables Idea: You can think of a random variable as a numerical measurement assigned to each outcome of a random experiment. Example: if you bet $100 on red in a spin of a roulette wheel, the outcome of the random experiment (the spin of the wheel) is one of { red, black, neutral } , but you are probably more interested in X , the amount you gain: X ( { red } ) = 100 , X ( { black } ) = X ( { neutral } ) = - 100 . Here, X is a random variable. Definition: Given a sample space Ω, a random variable X is a function that assigns to each outcome ω Ω a real number X ( ω ). NOTE: 1. A random variable is discrete if its possible values (its range) form a finite or countably infinite set of real numbers. For definiteness, let R ( X ) denote the range of X . 2. Random variable is continuous if it can takes values in an interval. 3. Random variables are denoted by capital letters while their values are denoted by lower case letters. E.g:- X- random variable, x- value. Examples: 1. Rolling two six sided dice. Let X - the sum of the two numbers .
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  • Spring '16
  • shichao liu
  • Probability theory, Geometric distribution, random variable X

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