Question

Roughly sketch the shapes of the following Gaussians N (μ,2). For each, you only need to show a representative contour line which is qualitatively accurate (has approximately the right orientation, for instance). 1 0.75 b) μ-C) and Σ =(-0.75 )

Answer 1

library(MASS)

## a)
M=c(0,0)
M
S=matrix(c(9,0,0,1), nrow=2)
S

bivn=mvrnorm(n = 1000, mu=M, Sigma=S)

# now we do a kernel density estimate
bivn.kde <- kde2d(bivn[,1], bivn[,2], n = 50)

# now plot your results
contour(bivn.kde)

## b)
M=c(0,0)
M
S.2=matrix(c(1,-0.75,-0.75,1), nrow=2)
S.2

bivn.2=mvrnorm(n = 1000, mu=M, Sigma=S.2)

# now we do a kernel density estimate
bivn.kde.2 <- kde2d(bivn.2[,1], bivn.2[,2], n = 50)

# now plot your results
contour(bivn.kde.2)