GE 331-Lecture 7

GE 331-Lecture 7 - Discrete Random Variables IE 300/GE 331...

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IE 300/GE 331 Lecture 7 Negar Kiyavash, UIUC 1 Discrete Random Variables

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IE 300/GE 331 Lecture 7 Negar Kiyavash, UIUC 2 Motivation (cont) sample space Real number line Example A coin is flipped three times. The sample space for this experiment is ={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Let random variable X be the number of heads in three coin tosses. X assigns each outcome in a number from the set {0, 1, 2, 3}. HHH HHT HTH HTT THH THT TTH TTT 3 2 2 1 2 1 1 0 There is nothing random about the Mapping!
IE 300/GE 331 Lecture 7 Negar Kiyavash, UIUC 3 Random Variables X maps w єΩ to the number X(w) The random variable is always denoted as X , never as X(w) X(w) means the number assigned to the outcome w, e.g. X(HHH) is 3 (nothing random) X is the random variable — one of its possible values is 3

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IE 300/GE 331 Lecture 7 Negar Kiyavash, UIUC 4 Random Variables Two or more outcomes could have the same image but each outcome has exactly one image HHH HHT HTH HTT THH THT TTH TTT 3 2 2 1 2 1 1 0 Consider the experiment consisting of tossing a coin till a Tail appears for the first time. X is the number of tosses on the trial X takes on values 1, 2, 3, 4, …
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GE 331-Lecture 7 - Discrete Random Variables IE 300/GE 331...

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