library(tidyverse)
  library(dplyr)
  library(reshape2)
  nu=100000
  nhere=100000
  datamerge930b=data.frame(cbind((rchisq(nhere,nu)-  nu)/sqrt(2*nu),rnorm(nhere, mean=0, sd=1)))
 colnames(datamerge930b)=c('chisquared', 'stdnorm')
 datamerge930b=melt(datamerge930b)

 datamerge930b%>%
 ggplot(aes(x = value, fill = variable)) + geom_density(alpha=0.69)+
 scale_fill_manual( values =c("dodgerblue4",'firebrick4'),
               name="distributions",
                    breaks=c("chisquared","stdnorm"),
                     labels=c("chi-squared","standard norm"))+
 ggtitle('u03bd=100000') +theme_minimal()+ theme(plot.title =    element_text(hjust = 0.5), text = element_text(size=16))