3

What it the distribution for square root of sum of squares of two independent normal distributed random variable? Assuming they have zero mean and same non-zero variance. Suppose $X$ and $Y$ ~ $N(0,\sigma^2)$, what is the distribution for $Z = \sqrt{X^2+Y^2}$? Looking for any feedbacks or comments.

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
FantasticAI
  • 417
  • 1
  • 4
  • 12
  • 2
    Hint: $X^2+Y^$ is an exponential random variable. – Dilip Sarwate May 16 '17 at 23:15
  • 2
    See https://en.wikipedia.org/wiki/Chi_distribution. – whuber May 16 '17 at 23:39
  • 4
    This reads like a textbook-style exercise (it's certainly simple enough to be one). In any case "looking for any feedback" is a bit too general (you didn't do anything to give feedback on). Can you be more explicit about the source of the problem? – Glen_b May 16 '17 at 23:56
  • This is related to the Raleigh distribution. That is $Z/\sigma$ has Raleigh distribution. I assume that you are taking the positive square root as is conventional. – Michael R. Chernick May 17 '17 at 00:40
  • Is there also a "named" distribution, if the expectation values of X and Y are non zero? – MiB_Coder Feb 02 '21 at 20:11

0 Answers0