cauchy

1. Calculating Cauchy's PDF, using domain definition drawings of F_X/Y(z)

Hi, I am trying to draw F (CDF of Cauchy) using X/Y relation for X,Y~N(0,1) iids and at some point very shortly I get lost. Especially because I don't know if I'm on the right direction. Could you direct me to the right way of solving this using the way I chose? So. Problem: Given X,Y~N(0,1)...
2. Haunted by Cauchy – A medium level problem

Hi Let's suppose X1 and X2 are two Normally distributed variables. [In general, X1 is from N(m1,s1^2) and X2 from N(m2, s2^2) where m1<m2 and s1^2≠s2^2.] However, let’s say, for the sake of starting the discussion, that both are Normally distributed N(1,2^2) and N(2,3^2). One of X1 or X2 is...
3. Deriving further values from regression coefficients

Hi, I’m hoping someone can help me. I’m trying to derive another value from the coefficients of two regression equations. I have 2 regression equations (for example) Miles traveled/year = α1 + β1X + δ1Y Fuel used/year = α2 + β2X + + δ2Y X = engine size and Y = tire pressure The...
4. plotting log likelihood function

Here is the code I am using to try to plot a log likelihood curve (cauchy distribution): X=rcauchy(10) h <- function(x) log(1+(x-X[1])^2) + ... + log(1+(x-X[10])^2) curve(h, from = -8, to = 7) But I get the error message 'Error in h(x) : '...' used in an incorrect context' How do...
5. Need help with joint distribution involving cauchy distributions

Okay so I know that help is only given to those who show effort, but I'm totally stuck on this one, I don't even know where to start. I know what the Cauchy distribution is and i could plug it in for the Y variables, but I don't know where that would get me. Please help me out!