Random Variables and Probability

microtus_mutiplex_voles<-c(2145 ,2237, 2250 ,2270,2300, 2300, 2305, 2305, 2305, 2330, 2330,2340, 2345, 2345, 2345, 2350, 2350, 2352, 2355, 2355, 2370, 2370,2370,2385, 2385, 2388, 2390, 2396, 2410, 2435, 2445, 2452, 2457, 2465, 2470,2470, 2475, 2500, 2500, 2525, 2535, 2590, 2600)
m<-mean(microtus_mutiplex_voles)
std<-sqrt(var(microtus_mutiplex_voles))

hist(microtus_mutiplex_voles, prob=TRUE, xlab="length", ylab="percent", main="Histogram for Vole Skull Lengths") 

m

## [1] 2385.977

std

## [1] 93.31909

### density=20, breaks=20, ylim=c(0, 0.7),
### curve(dnorm(x, mean=m, sd=std), col="red", lwd=3, add=TRUE) 

the density function curve

cmpute the area under the curve to get the probabilites

hist(microtus_mutiplex_voles, prob=TRUE, xlab="length", ylab="percent", main="Histogram and Normal density for Vole Skull Lengths")
curve(dnorm(x, mean=m, sd=std), col="red", lwd=3, add=TRUE)