x=c(4,5,6,7,8,9)

p=c(1/12,1/12,1/4,1/4,1/6,1/6)

plot(x,p,type="h",lwd=2,col='red')

plot of chunk unnamed-chunk-1

mu=sum(x*p)
mu
## [1] 6.833
var=sum(x^2*p)-mu^2
sigma=sqrt(var)
sigma
## [1] 1.462