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Why are random variables needed?

  1. Jan 12, 2010 #1
    please corret me if i am incorrect in my understanding of a RV,PMF or anything else but as i understand it a random variable simply maps a expirmental outcome to a real number. And a probability mass function simply gives the probabilty that a number will occur.

    Now my question is this: why cant we simply map a expiremental outcome to a probability rather than use a random variable to map from the sample space a to a real number then the map a real number to a probability via the PMF?
  2. jcsd
  3. Jan 12, 2010 #2
    a random variable is a function of the experimental outcomes. It is convenient not to redefine your probability distribution in terms of every random variable but to keep a fixed probability distribution and then look at the statistics of different random variables.
  4. Jan 12, 2010 #3
    Ahh this is what i suspected... So its fair to say that the RV helps keeps the pdf independent of each expirment
  5. Jan 13, 2010 #4

    Typically in statistics you look at sampling distributions. The sample mean and variance are example of random variables on the sampling distribution. If one knows something about the original distribution - say that is is normally distributed - then you know something about the distribution of the mean and the variance.
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