3AM stats quiz

by [anonymous]1 min read22nd Aug 20159 comments

3

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Because I'm tired and easily amused.

 

  1. Consider two independent, normally-distributed variables X and Y, each with a mean of 0.
    • X has a standard deviation of 4.
    • Y has a standard deviation of 1.
  2. Consider the probability distribution function (in two dimensions) for <X, Y>.
  3. Imagine contour lines on the PDF connecting points of equal probability density.  These would be a series of concentric ellipses.
  4. Draw the contour line that is tangent to the line X = 4.
  5. What values of Y does it pass through when X = 0?
  6. Post your answer.
  7. Run this R code to plot the contours:

library(mvtnorm) 
bivn <- mvrnorm(100000, mu = c(0, 0), Sigma = matrix(c(4, 0, 0, 1), 2, 2))
bivn.kde <- kde2d(bivn[,1], bivn[,2], n = 100)
image(bivn.kde); contour(bivn.kde, add = T)