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Make F RV by using 2 normal?

  1. Oct 29, 2014 #1
    I don't know if this is possible or not, let's see if this is a fun problem.

    Let X_1 and X_2 be 2 independent normal random variables. They have different means and variances, and they are independent. I want to have a function that inputs X_1 and X_2, and it has a F distribution with degree of freedom 1,1.

    We know the ratio of 2 mean squared errors are F distributed from ANOVA. But only 2 variables is hard to have means squared errors. How about other functional forms can make these two normals into F?
  2. jcsd
  3. Oct 31, 2014 #2

    Stephen Tashi

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    Science Advisor

    Your terminology for the inputs and outputs is somewhat ambiguous. There is a difference between "a random variable" and "a realization of a random variable" (i.e. a sample). If you input "a random variable X_1", the input would be distribution. If you input "a realization of a random variable X_1" then the input would be a single number.
  4. Oct 31, 2014 #3
    [itex](X_1^2+X_2^2)/(X_1-X_2)^2[/itex] is a non-central F random variable. But the non-central parameter is unknown.
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