K unf qrafvgl N rkc(-k^2 / 32) jurer N = 1/(4 fdeg(2*cv))
L unf qrafvgl O rkc(-l^2 / 2) jurer O = 1/fdeg(2cv)
Fvapr gurl’er vaqrcraqrag gur wbvag qrafvgl vf gur cebqhpg bs gur vaqvivqhny qrafvgvrf, anzryl NO * rkc(-k^2 / 32 - l^2 / 2). Urapr, gur pbagbhe yvarf fngvfsl -k^2 / 32 - l^2 / 2 = pbafgnag. Nofbeovat gur artngvir vagb gur pbafgnag, jr trg k^2 / 32 + l^2 / 2 = pbafgnag, juvpu vf na ryyvcfr jvgu nkrf cnenyyry gb gur pbbeqvangr nkrf.
Guvf vf gnatrag gb gur yvar K = 4 ng gur cbvag (4,0). Fhofgvghgvat vagb gur rdhngvba sbe gur ryyvcfr, jr svaq gung gur pbafgnag vf 1⁄2, fb k^2 / 32 + l^2 / 2 = 1⁄2. Frggvat k = 0 naq fbyivat sbe l, jr svaq gung l = 1.
You’re right. That’s what I expected, but not the answer I was getting. I was plotting bivariate distributions, it was 3AM, and a parameter that I thought was a standard deviation was a variance.
Used rot13 to avoid spoilers:
K unf qrafvgl N rkc(-k^2 / 32) jurer N = 1/(4 fdeg(2*cv))
L unf qrafvgl O rkc(-l^2 / 2) jurer O = 1/fdeg(2cv)
Fvapr gurl’er vaqrcraqrag gur wbvag qrafvgl vf gur cebqhpg bs gur vaqvivqhny qrafvgvrf, anzryl NO * rkc(-k^2 / 32 - l^2 / 2). Urapr, gur pbagbhe yvarf fngvfsl -k^2 / 32 - l^2 / 2 = pbafgnag. Nofbeovat gur artngvir vagb gur pbafgnag, jr trg k^2 / 32 + l^2 / 2 = pbafgnag, juvpu vf na ryyvcfr jvgu nkrf cnenyyry gb gur pbbeqvangr nkrf.
Guvf vf gnatrag gb gur yvar K = 4 ng gur cbvag (4,0). Fhofgvghgvat vagb gur rdhngvba sbe gur ryyvcfr, jr svaq gung gur pbafgnag vf 1⁄2, fb k^2 / 32 + l^2 / 2 = 1⁄2. Frggvat k = 0 naq fbyivat sbe l, jr svaq gung l = 1.
Small quibble: +- at the end.
[EDITED to be less spoilery.]
Of course. I seem to have overlooked that.
You’re right. That’s what I expected, but not the answer I was getting. I was plotting bivariate distributions, it was 3AM, and a parameter that I thought was a standard deviation was a variance.