Question

let (x,y) have uniform distribution on the four points (-1,0), (0,1), (0,-1), (1,0). show that x and y are uncorrelated but not independent

Answer 1

The x and y values in the given distribution are uncorrelated but not independent due to the normal distribution of y values for each x value.

Step-by-step explanation:

The given points (-1,0), (0,1), (0,-1), (1,0) represent a uniform distribution of (x,y) values. While x and y are uncorrelated, they are not independent. T

his is due to the fact that the distribution of y values for each x value is normally distributed about a line. The means of these normal distributions of y values lie on the line, indicating a dependency between x and y.