-------------------- # Blatt7, Aufg.2 # -------------------- # 2a) N = 10000 n = 10 # 2b) lambdaML = rep(0,N) lambda = 4 for( k in 1:N ) { x = rexp(n,rate=lambda) lambdaML[k] = 1/( 1/n * sum(x) ) } # 2c) ElambdaML = mean(lambdaML) ElambdaML n/(n-1)*lambda # theoretisches Resultat VlambdaML = var(lambdaML) VlambdaML n^2/((n-1)^2*(n-2))*lambda^2 # theoretisches Resultat # 2d) dlambdaML = function( x, n, lambda ) { res = (n*lambda)^n/factorial(n-1) res = res/x^(n+1) res = res*exp(-n*lambda/x) return(res) } hist(lambdaML,breaks=80,prob=TRUE) curve(dlambdaML(x,n=10,lambda=4),add=TRUE,col="red")