1

Let $A$ and $B$ be independent and normally distributed variables where $A \sim \mathcal{N}(\mu_1,\sigma_1^2)$ and $B \sim \mathcal{N}(\mu_2,\sigma_2^2)$.

What will be the density of $A^2 + B^2 -2AB\cos(\phi)$, where $\phi$ is a constant?

I read the answer in Finding the distribution of $5X_{1}^2+2X_{1}X_{2}+X_{2}^2$ , applying the same trick will result in the sum of two scaled non-central and dependent chi-squares.

Community
  • 1
Anas Alhashimi
  • 63
  • I can't quite understand the question. Are you asking about the pdf of the sampling distribution of the Euclidean distance (a scalar) between two correlated variables (realized in some sample size n) with correlation $\phi$? – ttnphns Feb 22 '17 at 13:24
  • Actually I have a sensor that measures the distances and angles of two arbitrary placed land marks $L_A$ and $L_B$. I would like to find an unbiased estimator for the distance between the two land marks $d_{AB}$. So I have the distance measurements are normally distributed and the angle difference $\phi$ assumed noiseless for simplicity. – Anas Alhashimi Feb 22 '17 at 16:00
  • The same "trick" applies to your situation, doesn't it? All you have to do is change the numbers. – whuber Feb 22 '17 at 23:48

0 Answers0