Because Iām tired and easily amused.
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.
Consider the probability distribution function (in two dimensions) for <X, Y>.
Imagine contour lines on the PDF connecting points of equal probability density. These would be a series of concentric ellipses.
Draw the contour line that is tangent to the line X = 4.
What values of Y does it pass through when X = 0?
Post your answer.
Run this R code to plot the contours:
3AM stats quiz
Because Iām tired and easily amused.
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.
Consider the probability distribution function (in two dimensions) for <X, Y>.
Imagine contour lines on the PDF connecting points of equal probability density. These would be a series of concentric ellipses.
Draw the contour line that is tangent to the line X = 4.
What values of Y does it pass through when X = 0?
Post your answer.
Run this R code to plot the contours: