mm4 - Aphenomenonisrandomifindividualoutcomesare

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 A phenomenon is  random  if individual outcomes are  uncertain but there is nonetheless a regular distribution of  outcomes in a large number of repetitions.  Randomness requires a long series of  independent trials .  The  probability  of any outcome of a random phenomenon  is the proportion of times the outcome would occur in a very  long series of  independent  repetitions.  That is, probability is  a long-term relative frequency of independent repetitions.
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 Thus, the chance of something gives the  percentage of time it is expected to happen,  conditions.
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A probability model is based on  independent  trials.  Besides independent trials, it requires:   A list of possible outcomes of the random  phenomenon:  the sample space .  A probability for each outcome or set of outcomes —each   event of the random phenomenon.
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Think of the probability model as  box model . See Freedman et al.,  Statistics .
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  E.g., someone has a set of 10 cards consisting  of three cards with #1, one card with #2, two cards  mixed well.   We make 5 draws from the box. After each  remixed.  For each draw, what are the chances of  drawing the following numbers: 1, 2, 3, 4, 5, 6, 7,  8, 9, 10?
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Card # Probability (for  each card drawn) 1 .30 2 .10 4 .20 7 .20 8 .10 10 .10 Sum of event probabilities=1.0
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 How did we compute the  probabilities for the box model?
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We did so:  By making a list of the possible outcomes of the  random phenomenon:  the sample space  By assigning a probability for each outcome (or  set of outcomes) of the random phenomenon—for  each  event .
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0 .1 .2 .3 Probability 1 2 4 7 8 10 Card Number
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. input cardnum prob 1. 1 .3 2. 2 .1 3. 4 .2 4. 7 .2 5. 8 .1 6. 10 .1 7. end  Create the variables
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. gr bar prob, over(cardnum) 0 .1 .2 .3 Probability 1 2 4 7 8 10 Card Number
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  To be valid, the assigned  probabilities must be premised on  independent, random  draws (i.e.  independent, randomly drawn  observations).
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 In the previous example about card values,  consider the set of cards as a population.  What we did, then, was draw a sample from  that population.  What was the basis of the mean of the sample 
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mm4 - Aphenomenonisrandomifindividualoutcomesare

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