R Markdown

Este TP consiste na implementaçãoo (em linguagem R) e execução de métodos de geraçaõ de variáveis aleatórias. As seguintes tarefas devem ser realizadas: 1) Implementar o método congruencial para geração de variável aleatória uniforme no intervalo (0,1). 2) Implementar o método polar para geração de variável aleatória normal padrão. 2) Construir tabela de probabilidades acumuladas da variável normal padrão utilizando (1) método de integração de Monte Carlo e (2) através da estimativa da probabilidade acumulada obtida pela amostra gerada pelo método polar.

Códigos

gera_uniformes<-function(n){
  #browser()
  a<-16807
  m<- 2^31 -1
  
  x0<-100
  y<-numeric(n)
  x<-numeric(n)
  
  for (i in 1:n) {
    
    if(i==1) {
      
      x[1] <-(a*x0) %% m
      y[1] <-x[1]/m
      # print(i)
    }
    else {
      #   print(i)
      
      x[i] <-(a*x[i-1]) %% m
      
      y[i] <-x[i]/m
      
    }
    
  }
  return(y)
  
}



# Definindo Monte Carlo para calcular integral no interval [0 ; 1]

#Passos
# P1: gerar vetor de uniformes u
# P2: cálculo de g(u),onde a função g é definida por qual distribuição se quer calcular

# Definindo Monte Carlo para calcular integral em intervalo qualquer.

# Gerar n uniformes
calcula_prob<-function(min,max,metodo){
#browser()
a<-min
c<- seq(0,max,by=0.01)
metodo<-metodo

if (metodo=="montecarlo"){
  return(calcula_prob_montecarlo(a,c))
}
  else{
    return(calcula_prob_polar(a,c))
  }
}

# # gera uniformes em [0,1]
calcula_prob_montecarlo_01 <-function(n){
  u<-gera_uniformes(n)
  gx<- (1/(sqrt(2*pi)))*exp(-0.5*u^2)
  prob <-mean(gx)
  
  return(prob)
}

calcula_prob_montecarlo <-function(a,c){
  acum<-numeric(length(c))
  
  #browser()
  u<-gera_uniformes(100000)#*c[i]
  
  for (i in seq_along(c)){
    # gera uniformes em [0,c]
    #u<-gera_uniformes(100)*c[i]
  
    b<-c[i]
    gx<-u*(b-a)+a
    
    hy<- (1/(sqrt(2*pi)))*exp(-0.5*gx^2)*(b-a)
    #hy<-(gx^3)*(b-a)
    acum[i]<-mean(hy)
  }
  return(list(acum,c))
}


calcula_prob_polar <-function(a,c){
  #browser()
  x<-numeric(length(c))
  temp<-numeric(length(c))

  u1<-gera_uniformes(10000)#*c[i]
  u2<-gera_uniformes(10000)#*c[i]
  
  v1<-2*u1-1
  v2<-2*u2-1

  raio<-numeric(length(u1))
  
  raio<-v1^2 + v2^2
  
  prob<-numeric(length(c))
  #browser()
   
  for (i in seq_along(u1)){
    
    if (raio[i] <1 & raio[i]!=0) {
      x[i] <-sqrt(-2*log(raio[i])/raio[i])*v1[i]
    }
   
  }

     x<-x[!is.na(x)]
   for (i in seq_along(c)){
     prob[i]=(sum(x<c[i]))/length(x)
   }
   
  return(list(prob,c,x))
}


u<-gera_uniformes(100)

gx<- (1/(sqrt(2*pi)))*exp(-0.5*u^2)

mi_medio1 <-mean(gx)


resul <-calcula_prob(0,3.99,"polar")
prob<-unlist(resul[1])
x<-unlist(resul[2])

for(i in 1:400){ print(c(prob[i],x[i]))}
## [1] 0.4937116 0.0000000
## [1] 0.5106205 0.0100000
## [1] 0.5106205 0.0200000
## [1] 0.5108999 0.0300000
## [1] 0.5110397 0.0400000
## [1] 0.5111794 0.0500000
## [1] 0.5113192 0.0600000
## [1] 0.5115987 0.0700000
## [1] 0.5120179 0.0800000
## [1] 0.5124371 0.0900000
## [1] 0.5128563 0.1000000
## [1] 0.5136948 0.1100000
## [1] 0.5139743 0.1200000
## [1] 0.5143935 0.1300000
## [1] 0.5148127 0.1400000
## [1] 0.5153717 0.1500000
## [1] 0.5162102 0.1600000
## [1] 0.5167691 0.1700000
## [1] 0.5183063 0.1800000
## [1] 0.519005 0.190000
## [1] 0.5202627 0.2000000
## [1] 0.5208217 0.2100000
## [1] 0.5219396 0.2200000
## [1] 0.5233371 0.2300000
## [1] 0.524455 0.240000
## [1] 0.5252935 0.2500000
## [1] 0.5266909 0.2600000
## [1] 0.5276691 0.2700000
## [1] 0.5286473 0.2800000
## [1] 0.5297652 0.2900000
## [1] 0.5304639 0.3000000
## [1] 0.5321409 0.3100000
## [1] 0.5340973 0.3200000
## [1] 0.5354947 0.3300000
## [1] 0.5373113 0.3400000
## [1] 0.5387088 0.3500000
## [1] 0.5408049 0.3600000
## [1] 0.5424818 0.3700000
## [1] 0.5442985 0.3800000
## [1] 0.5454164 0.3900000
## [1] 0.5470933 0.4000000
## [1] 0.5487703 0.4100000
## [1] 0.5503074 0.4200000
## [1] 0.5515651 0.4300000
## [1] 0.5529625 0.4400000
## [1] 0.5547792 0.4500000
## [1] 0.5564561 0.4600000
## [1] 0.5589715 0.4700000
## [1] 0.5616266 0.4800000
## [1] 0.5631638 0.4900000
## [1] 0.5653997 0.5000000
## [1] 0.5674958 0.5100000
## [1] 0.569592 0.520000
## [1] 0.5715484 0.5300000
## [1] 0.5740637 0.5400000
## [1] 0.5760201 0.5500000
## [1] 0.5786752 0.5600000
## [1] 0.5811906 0.5700000
## [1] 0.5834265 0.5800000
## [1] 0.5848239 0.5900000
## [1] 0.5871996 0.6000000
## [1] 0.5892957 0.6100000
## [1] 0.5930688 0.6200000
## [1] 0.5951649 0.6300000
## [1] 0.5976803 0.6400000
## [1] 0.6007546 0.6500000
## [1] 0.6035495 0.6600000
## [1] 0.607043 0.670000
## [1] 0.6094187 0.6800000
## [1] 0.6123533 0.6900000
## [1] 0.6157071 0.7000000
## [1] 0.618502 0.710000
## [1] 0.6219955 0.7200000
## [1] 0.6250699 0.7300000
## [1] 0.6292622 0.7400000
## [1] 0.632057 0.750000
## [1] 0.6347121 0.7600000
## [1] 0.6377865 0.7700000
## [1] 0.6397429 0.7800000
## [1] 0.6419788 0.7900000
## [1] 0.6457518 0.8000000
## [1] 0.6491056 0.8100000
## [1] 0.6520402 0.8200000
## [1] 0.6558133 0.8300000
## [1] 0.6590274 0.8400000
## [1] 0.6623812 0.8500000
## [1] 0.6654556 0.8600000
## [1] 0.6681107 0.8700000
## [1] 0.6716042 0.8800000
## [1] 0.6739799 0.8900000
## [1] 0.676076 0.900000
## [1] 0.6787311 0.9100000
## [1] 0.6811068 0.9200000
## [1] 0.6841811 0.9300000
## [1] 0.6854388 0.9400000
## [1] 0.6886529 0.9500000
## [1] 0.691867 0.960000
## [1] 0.6942426 0.9700000
## [1] 0.696758 0.980000
## [1] 0.7009503 0.9900000
## [1] 0.7047233 1.0000000
## [1] 0.7064002 1.0100000
## [1] 0.7084964 1.0200000
## [1] 0.7115707 1.0300000
## [1] 0.716322 1.040000
## [1] 0.7196758 1.0500000
## [1] 0.7233091 1.0600000
## [1] 0.7270822 1.0700000
## [1] 0.7311347 1.0800000
## [1] 0.7339296 1.0900000
## [1] 0.7371437 1.1000000
## [1] 0.739659 1.110000
## [1] 0.7414757 1.1200000
## [1] 0.7442705 1.1300000
## [1] 0.7481833 1.1400000
## [1] 0.7513974 1.1500000
## [1] 0.7547513 1.1600000
## [1] 0.7564282 1.1700000
## [1] 0.7599217 1.1800000
## [1] 0.7632756 1.1900000
## [1] 0.7664897 1.2000000
## [1] 0.769564 1.210000
## [1] 0.7717999 1.2200000
## [1] 0.774455 1.230000
## [1] 0.7771101 1.2400000
## [1] 0.7804639 1.2500000
## [1] 0.7828396 1.2600000
## [1] 0.7861934 1.2700000
## [1] 0.7892677 1.2800000
## [1] 0.7912241 1.2900000
## [1] 0.7929011 1.3000000
## [1] 0.7951369 1.3100000
## [1] 0.7979318 1.3200000
## [1] 0.8005869 1.3300000
## [1] 0.803242 1.340000
## [1] 0.8061766 1.3500000
## [1] 0.8088317 1.3600000
## [1] 0.8113471 1.3700000
## [1] 0.813583 1.380000
## [1] 0.8172163 1.3900000
## [1] 0.819592 1.400000
## [1] 0.8222471 1.4100000
## [1] 0.8249022 1.4200000
## [1] 0.8274176 1.4300000
## [1] 0.8292342 1.4400000
## [1] 0.8311906 1.4500000
## [1] 0.832588 1.460000
## [1] 0.8346842 1.4700000
## [1] 0.8369201 1.4800000
## [1] 0.8401342 1.4900000
## [1] 0.8426495 1.5000000
## [1] 0.8453046 1.5100000
## [1] 0.84782 1.52000
## [1] 0.8504751 1.5300000
## [1] 0.8528508 1.5400000
## [1] 0.8546674 1.5500000
## [1] 0.8564841 1.5600000
## [1] 0.8599776 1.5700000
## [1] 0.8620738 1.5800000
## [1] 0.8645892 1.5900000
## [1] 0.8664058 1.6000000
## [1] 0.8697596 1.6100000
## [1] 0.871716 1.620000
## [1] 0.8735327 1.6300000
## [1] 0.8764673 1.6400000
## [1] 0.8780045 1.6500000
## [1] 0.8796814 1.6600000
## [1] 0.8810788 1.6700000
## [1] 0.8841532 1.6800000
## [1] 0.8856903 1.6900000
## [1] 0.888066 1.700000
## [1] 0.8897429 1.7100000
## [1] 0.8914198 1.7200000
## [1] 0.8930967 1.7300000
## [1] 0.8951928 1.7400000
## [1] 0.8974287 1.7500000
## [1] 0.8995249 1.7600000
## [1] 0.9013415 1.7700000
## [1] 0.9031582 1.7800000
## [1] 0.9051146 1.7900000
## [1] 0.906512 1.800000
## [1] 0.9091671 1.8100000
## [1] 0.9097261 1.8200000
## [1] 0.9105646 1.8300000
## [1] 0.9121017 1.8400000
## [1] 0.9137786 1.8500000
## [1] 0.9148966 1.8600000
## [1] 0.9158748 1.8700000
## [1] 0.916853 1.880000
## [1] 0.9182504 1.8900000
## [1] 0.9202068 1.9000000
## [1] 0.9221632 1.9100000
## [1] 0.9239799 1.9200000
## [1] 0.9257965 1.9300000
## [1] 0.9263555 1.9400000
## [1] 0.9278927 1.9500000
## [1] 0.9297093 1.9600000
## [1] 0.9308273 1.9700000
## [1] 0.9318055 1.9800000
## [1] 0.9340414 1.9900000
## [1] 0.9354388 2.0000000
## [1] 0.936417 2.010000
## [1] 0.9378144 2.0200000
## [1] 0.9399106 2.0300000
## [1] 0.9408888 2.0400000
## [1] 0.9417272 2.0500000
## [1] 0.9431247 2.0600000
## [1] 0.9446618 2.0700000
## [1] 0.9463387 2.0800000
## [1] 0.9477362 2.0900000
## [1] 0.9487144 2.1000000
## [1] 0.9495528 2.1100000
## [1] 0.9501118 2.1200000
## [1] 0.9502515 2.1300000
## [1] 0.9512297 2.1400000
## [1] 0.9523477 2.1500000
## [1] 0.9545836 2.1600000
## [1] 0.9558413 2.1700000
## [1] 0.9575182 2.1800000
## [1] 0.9583566 2.1900000
## [1] 0.9589156 2.2000000
## [1] 0.9598938 2.2100000
## [1] 0.9604528 2.2200000
## [1] 0.9611515 2.2300000
## [1] 0.9625489 2.2400000
## [1] 0.9633874 2.2500000
## [1] 0.9645053 2.2600000
## [1] 0.9650643 2.2700000
## [1] 0.965763 2.280000
## [1] 0.9667412 2.2900000
## [1] 0.9674399 2.3000000
## [1] 0.9681386 2.3100000
## [1] 0.9688373 2.3200000
## [1] 0.9696758 2.3300000
## [1] 0.971213 2.340000
## [1] 0.9723309 2.3500000
## [1] 0.9738681 2.3600000
## [1] 0.9741476 2.3700000
## [1] 0.9745668 2.3800000
## [1] 0.9754053 2.3900000
## [1] 0.9758245 2.4000000
## [1] 0.9766629 2.4100000
## [1] 0.9775014 2.4200000
## [1] 0.9779206 2.4300000
## [1] 0.9787591 2.4400000
## [1] 0.9787591 2.4500000
## [1] 0.9788988 2.4600000
## [1] 0.9791783 2.4700000
## [1] 0.9793181 2.4800000
## [1] 0.9795975 2.4900000
## [1] 0.9801565 2.5000000
## [1] 0.9802963 2.5100000
## [1] 0.980436 2.520000
## [1] 0.9805757 2.5300000
## [1] 0.9808552 2.5400000
## [1] 0.9808552 2.5500000
## [1] 0.980995 2.560000
## [1] 0.9821129 2.5700000
## [1] 0.9821129 2.5800000
## [1] 0.9823924 2.5900000
## [1] 0.9826719 2.6000000
## [1] 0.9830911 2.6100000
## [1] 0.9836501 2.6200000
## [1] 0.9837898 2.6300000
## [1] 0.9839296 2.6400000
## [1] 0.9844885 2.6500000
## [1] 0.9850475 2.6600000
## [1] 0.985327 2.670000
## [1] 0.9857462 2.6800000
## [1] 0.985886 2.690000
## [1] 0.9860257 2.7000000
## [1] 0.9864449 2.7100000
## [1] 0.9865847 2.7200000
## [1] 0.9865847 2.7300000
## [1] 0.9870039 2.7400000
## [1] 0.9874231 2.7500000
## [1] 0.9875629 2.7600000
## [1] 0.9877026 2.7700000
## [1] 0.9878424 2.7800000
## [1] 0.9881219 2.7900000
## [1] 0.9884013 2.8000000
## [1] 0.9885411 2.8100000
## [1] 0.9891001 2.8200000
## [1] 0.9893795 2.8300000
## [1] 0.9897988 2.8400000
## [1] 0.9900783 2.8500000
## [1] 0.9903577 2.8600000
## [1] 0.990777 2.870000
## [1] 0.990777 2.880000
## [1] 0.9909167 2.8900000
## [1] 0.9910565 2.9000000
## [1] 0.9914757 2.9100000
## [1] 0.9916154 2.9200000
## [1] 0.9917552 2.9300000
## [1] 0.9917552 2.9400000
## [1] 0.9917552 2.9500000
## [1] 0.9918949 2.9600000
## [1] 0.9920347 2.9700000
## [1] 0.9923141 2.9800000
## [1] 0.9923141 2.9900000
## [1] 0.9927334 3.0000000
## [1] 0.9930129 3.0100000
## [1] 0.9931526 3.0200000
## [1] 0.9932923 3.0300000
## [1] 0.9937116 3.0400000
## [1] 0.9941308 3.0500000
## [1] 0.9941308 3.0600000
## [1] 0.9942705 3.0700000
## [1] 0.9944103 3.0800000
## [1] 0.9944103 3.0900000
## [1] 0.99455 3.10000
## [1] 0.9946898 3.1100000
## [1] 0.9948295 3.1200000
## [1] 0.9948295 3.1300000
## [1] 0.995109 3.140000
## [1] 0.9953885 3.1500000
## [1] 0.9953885 3.1600000
## [1] 0.9953885 3.1700000
## [1] 0.9953885 3.1800000
## [1] 0.9955282 3.1900000
## [1] 0.9958077 3.2000000
## [1] 0.9959475 3.2100000
## [1] 0.9959475 3.2200000
## [1] 0.9962269 3.2300000
## [1] 0.9962269 3.2400000
## [1] 0.9965064 3.2500000
## [1] 0.9966462 3.2600000
## [1] 0.9966462 3.2700000
## [1] 0.9967859 3.2800000
## [1] 0.9969257 3.2900000
## [1] 0.9972051 3.3000000
## [1] 0.9973449 3.3100000
## [1] 0.9974846 3.3200000
## [1] 0.9974846 3.3300000
## [1] 0.9974846 3.3400000
## [1] 0.9976244 3.3500000
## [1] 0.9976244 3.3600000
## [1] 0.9977641 3.3700000
## [1] 0.9980436 3.3800000
## [1] 0.9981833 3.3900000
## [1] 0.9981833 3.4000000
## [1] 0.9981833 3.4100000
## [1] 0.9983231 3.4200000
## [1] 0.9983231 3.4300000
## [1] 0.9983231 3.4400000
## [1] 0.9983231 3.4500000
## [1] 0.9983231 3.4600000
## [1] 0.9983231 3.4700000
## [1] 0.9983231 3.4800000
## [1] 0.9984628 3.4900000
## [1] 0.9986026 3.5000000
## [1] 0.9986026 3.5100000
## [1] 0.9986026 3.5200000
## [1] 0.9988821 3.5300000
## [1] 0.9988821 3.5400000
## [1] 0.9988821 3.5500000
## [1] 0.9990218 3.5600000
## [1] 0.9990218 3.5700000
## [1] 0.9990218 3.5800000
## [1] 0.9990218 3.5900000
## [1] 0.9990218 3.6000000
## [1] 0.9990218 3.6100000
## [1] 0.9991615 3.6200000
## [1] 0.9991615 3.6300000
## [1] 0.9991615 3.6400000
## [1] 0.9991615 3.6500000
## [1] 0.9991615 3.6600000
## [1] 0.9991615 3.6700000
## [1] 0.9993013 3.6800000
## [1] 0.9993013 3.6900000
## [1] 0.999441 3.700000
## [1] 0.999441 3.710000
## [1] 0.999441 3.720000
## [1] 0.999441 3.730000
## [1] 0.999441 3.740000
## [1] 0.999441 3.750000
## [1] 0.999441 3.760000
## [1] 0.999441 3.770000
## [1] 0.9995808 3.7800000
## [1] 0.9995808 3.7900000
## [1] 0.9995808 3.8000000
## [1] 0.9995808 3.8100000
## [1] 0.9995808 3.8200000
## [1] 0.9995808 3.8300000
## [1] 0.9995808 3.8400000
## [1] 0.9995808 3.8500000
## [1] 0.9995808 3.8600000
## [1] 0.9995808 3.8700000
## [1] 0.9995808 3.8800000
## [1] 0.9995808 3.8900000
## [1] 0.9995808 3.9000000
## [1] 0.9997205 3.9100000
## [1] 0.9997205 3.9200000
## [1] 0.9997205 3.9300000
## [1] 0.9997205 3.9400000
## [1] 0.9997205 3.9500000
## [1] 0.9997205 3.9600000
## [1] 0.9997205 3.9700000
## [1] 0.9997205 3.9800000
## [1] 0.9997205 3.9900000
erro<--prob+pnorm(seq(0,3.99,0.01))
b<-seq(0,3.99,0.01)
plot(b,erro,main="Gráfico erro -Verificar correção do gráfico-")

resul2 <-calcula_prob(0,3.99,"montecarlo")

prob<-unlist(resul2[1])+0.5
x<-unlist(resul2[2])

for(i in 1:400){ print(c(prob[i],x[i]))}
## [1] 0.5 0.0
## [1] 0.5039894 0.0100000
## [1] 0.5079783 0.0200000
## [1] 0.5119665 0.0300000
## [1] 0.5159534 0.0400000
## [1] 0.5199388 0.0500000
## [1] 0.5239221 0.0600000
## [1] 0.5279031 0.0700000
## [1] 0.5318813 0.0800000
## [1] 0.5358563 0.0900000
## [1] 0.5398276 0.1000000
## [1] 0.5437951 0.1100000
## [1] 0.5477581 0.1200000
## [1] 0.5517164 0.1300000
## [1] 0.5556695 0.1400000
## [1] 0.559617 0.150000
## [1] 0.5635587 0.1600000
## [1] 0.567494 0.170000
## [1] 0.5714226 0.1800000
## [1] 0.5753441 0.1900000
## [1] 0.5792582 0.2000000
## [1] 0.5831644 0.2100000
## [1] 0.5870624 0.2200000
## [1] 0.5909518 0.2300000
## [1] 0.5948322 0.2400000
## [1] 0.5987034 0.2500000
## [1] 0.6025648 0.2600000
## [1] 0.6064161 0.2700000
## [1] 0.6102571 0.2800000
## [1] 0.6140873 0.2900000
## [1] 0.6179063 0.3000000
## [1] 0.6217139 0.3100000
## [1] 0.6255097 0.3200000
## [1] 0.6292932 0.3300000
## [1] 0.6330643 0.3400000
## [1] 0.6368226 0.3500000
## [1] 0.6405677 0.3600000
## [1] 0.6442993 0.3700000
## [1] 0.648017 0.380000
## [1] 0.6517206 0.3900000
## [1] 0.6554098 0.4000000
## [1] 0.6590842 0.4100000
## [1] 0.6627435 0.4200000
## [1] 0.6663874 0.4300000
## [1] 0.6700156 0.4400000
## [1] 0.6736278 0.4500000
## [1] 0.6772238 0.4600000
## [1] 0.6808032 0.4700000
## [1] 0.6843658 0.4800000
## [1] 0.6879113 0.4900000
## [1] 0.6914394 0.5000000
## [1] 0.6949498 0.5100000
## [1] 0.6984423 0.5200000
## [1] 0.7019167 0.5300000
## [1] 0.7053726 0.5400000
## [1] 0.7088098 0.5500000
## [1] 0.7122282 0.5600000
## [1] 0.7156273 0.5700000
## [1] 0.7190071 0.5800000
## [1] 0.7223673 0.5900000
## [1] 0.7257076 0.6000000
## [1] 0.7290279 0.6100000
## [1] 0.732328 0.620000
## [1] 0.7356075 0.6300000
## [1] 0.7388664 0.6400000
## [1] 0.7421044 0.6500000
## [1] 0.7453214 0.6600000
## [1] 0.7485171 0.6700000
## [1] 0.7516915 0.6800000
## [1] 0.7548442 0.6900000
## [1] 0.7579752 0.7000000
## [1] 0.7610842 0.7100000
## [1] 0.7641712 0.7200000
## [1] 0.7672359 0.7300000
## [1] 0.7702783 0.7400000
## [1] 0.7732981 0.7500000
## [1] 0.7762953 0.7600000
## [1] 0.7792698 0.7700000
## [1] 0.7822213 0.7800000
## [1] 0.7851498 0.7900000
## [1] 0.7880551 0.8000000
## [1] 0.7909373 0.8100000
## [1] 0.793796 0.820000
## [1] 0.7966314 0.8300000
## [1] 0.7994432 0.8400000
## [1] 0.8022314 0.8500000
## [1] 0.8049959 0.8600000
## [1] 0.8077366 0.8700000
## [1] 0.8104534 0.8800000
## [1] 0.8131464 0.8900000
## [1] 0.8158154 0.9000000
## [1] 0.8184604 0.9100000
## [1] 0.8210813 0.9200000
## [1] 0.8236782 0.9300000
## [1] 0.8262508 0.9400000
## [1] 0.8287993 0.9500000
## [1] 0.8313236 0.9600000
## [1] 0.8338237 0.9700000
## [1] 0.8362995 0.9800000
## [1] 0.838751 0.990000
## [1] 0.8411783 1.0000000
## [1] 0.8435813 1.0100000
## [1] 0.8459601 1.0200000
## [1] 0.8483146 1.0300000
## [1] 0.8506449 1.0400000
## [1] 0.8529509 1.0500000
## [1] 0.8552327 1.0600000
## [1] 0.8574903 1.0700000
## [1] 0.8597238 1.0800000
## [1] 0.8619332 1.0900000
## [1] 0.8641184 1.1000000
## [1] 0.8662797 1.1100000
## [1] 0.868417 1.120000
## [1] 0.8705303 1.1300000
## [1] 0.8726197 1.1400000
## [1] 0.8746854 1.1500000
## [1] 0.8767273 1.1600000
## [1] 0.8787455 1.1700000
## [1] 0.88074 1.18000
## [1] 0.8827111 1.1900000
## [1] 0.8846587 1.2000000
## [1] 0.8865829 1.2100000
## [1] 0.8884839 1.2200000
## [1] 0.8903616 1.2300000
## [1] 0.8922162 1.2400000
## [1] 0.8940479 1.2500000
## [1] 0.8958566 1.2600000
## [1] 0.8976426 1.2700000
## [1] 0.8994059 1.2800000
## [1] 0.9011466 1.2900000
## [1] 0.9028648 1.3000000
## [1] 0.9045607 1.3100000
## [1] 0.9062343 1.3200000
## [1] 0.9078859 1.3300000
## [1] 0.9095155 1.3400000
## [1] 0.9111232 1.3500000
## [1] 0.9127092 1.3600000
## [1] 0.9142736 1.3700000
## [1] 0.9158166 1.3800000
## [1] 0.9173383 1.3900000
## [1] 0.9188388 1.4000000
## [1] 0.9203183 1.4100000
## [1] 0.9217769 1.4200000
## [1] 0.9232147 1.4300000
## [1] 0.924632 1.440000
## [1] 0.9260289 1.4500000
## [1] 0.9274054 1.4600000
## [1] 0.9287619 1.4700000
## [1] 0.9300984 1.4800000
## [1] 0.931415 1.490000
## [1] 0.9327121 1.5000000
## [1] 0.9339896 1.5100000
## [1] 0.9352478 1.5200000
## [1] 0.9364868 1.5300000
## [1] 0.9377069 1.5400000
## [1] 0.9389081 1.5500000
## [1] 0.9400907 1.5600000
## [1] 0.9412548 1.5700000
## [1] 0.9424005 1.5800000
## [1] 0.9435281 1.5900000
## [1] 0.9446378 1.6000000
## [1] 0.9457296 1.6100000
## [1] 0.9468038 1.6200000
## [1] 0.9478605 1.6300000
## [1] 0.9489 1.6400
## [1] 0.9499224 1.6500000
## [1] 0.9509278 1.6600000
## [1] 0.9519165 1.6700000
## [1] 0.9528886 1.6800000
## [1] 0.9538443 1.6900000
## [1] 0.9547838 1.7000000
## [1] 0.9557073 1.7100000
## [1] 0.9566149 1.7200000
## [1] 0.9575068 1.7300000
## [1] 0.9583832 1.7400000
## [1] 0.9592443 1.7500000
## [1] 0.9600902 1.7600000
## [1] 0.9609212 1.7700000
## [1] 0.9617373 1.7800000
## [1] 0.9625389 1.7900000
## [1] 0.963326 1.800000
## [1] 0.9640989 1.8100000
## [1] 0.9648577 1.8200000
## [1] 0.9656026 1.8300000
## [1] 0.9663338 1.8400000
## [1] 0.9670514 1.8500000
## [1] 0.9677556 1.8600000
## [1] 0.9684466 1.8700000
## [1] 0.9691247 1.8800000
## [1] 0.9697898 1.8900000
## [1] 0.9704423 1.9000000
## [1] 0.9710823 1.9100000
## [1] 0.9717099 1.9200000
## [1] 0.9723254 1.9300000
## [1] 0.9729288 1.9400000
## [1] 0.9735205 1.9500000
## [1] 0.9741004 1.9600000
## [1] 0.9746689 1.9700000
## [1] 0.9752261 1.9800000
## [1] 0.9757721 1.9900000
## [1] 0.9763071 2.0000000
## [1] 0.9768313 2.0100000
## [1] 0.9773448 2.0200000
## [1] 0.9778478 2.0300000
## [1] 0.9783404 2.0400000
## [1] 0.9788228 2.0500000
## [1] 0.9792953 2.0600000
## [1] 0.9797578 2.0700000
## [1] 0.9802106 2.0800000
## [1] 0.9806538 2.0900000
## [1] 0.9810876 2.1000000
## [1] 0.9815122 2.1100000
## [1] 0.9819276 2.1200000
## [1] 0.9823341 2.1300000
## [1] 0.9827317 2.1400000
## [1] 0.9831207 2.1500000
## [1] 0.9835011 2.1600000
## [1] 0.9838731 2.1700000
## [1] 0.9842369 2.1800000
## [1] 0.9845926 2.1900000
## [1] 0.9849404 2.2000000
## [1] 0.9852803 2.2100000
## [1] 0.9856125 2.2200000
## [1] 0.9859371 2.2300000
## [1] 0.9862543 2.2400000
## [1] 0.9865642 2.2500000
## [1] 0.986867 2.260000
## [1] 0.9871627 2.2700000
## [1] 0.9874515 2.2800000
## [1] 0.9877336 2.2900000
## [1] 0.9880089 2.3000000
## [1] 0.9882778 2.3100000
## [1] 0.9885402 2.3200000
## [1] 0.9887963 2.3300000
## [1] 0.9890463 2.3400000
## [1] 0.9892902 2.3500000
## [1] 0.9895281 2.3600000
## [1] 0.9897602 2.3700000
## [1] 0.9899866 2.3800000
## [1] 0.9902074 2.3900000
## [1] 0.9904227 2.4000000
## [1] 0.9906326 2.4100000
## [1] 0.9908373 2.4200000
## [1] 0.9910367 2.4300000
## [1] 0.9912311 2.4400000
## [1] 0.9914205 2.4500000
## [1] 0.991605 2.460000
## [1] 0.9917848 2.4700000
## [1] 0.9919598 2.4800000
## [1] 0.9921303 2.4900000
## [1] 0.9922963 2.5000000
## [1] 0.992458 2.510000
## [1] 0.9926153 2.5200000
## [1] 0.9927684 2.5300000
## [1] 0.9929174 2.5400000
## [1] 0.9930623 2.5500000
## [1] 0.9932034 2.5600000
## [1] 0.9933405 2.5700000
## [1] 0.9934739 2.5800000
## [1] 0.9936036 2.5900000
## [1] 0.9937296 2.6000000
## [1] 0.9938521 2.6100000
## [1] 0.9939712 2.6200000
## [1] 0.9940869 2.6300000
## [1] 0.9941993 2.6400000
## [1] 0.9943084 2.6500000
## [1] 0.9944144 2.6600000
## [1] 0.9945173 2.6700000
## [1] 0.9946172 2.6800000
## [1] 0.9947141 2.6900000
## [1] 0.9948082 2.7000000
## [1] 0.9948994 2.7100000
## [1] 0.9949879 2.7200000
## [1] 0.9950737 2.7300000
## [1] 0.9951569 2.7400000
## [1] 0.9952375 2.7500000
## [1] 0.9953156 2.7600000
## [1] 0.9953913 2.7700000
## [1] 0.9954647 2.7800000
## [1] 0.9955356 2.7900000
## [1] 0.9956044 2.8000000
## [1] 0.9956709 2.8100000
## [1] 0.9957352 2.8200000
## [1] 0.9957975 2.8300000
## [1] 0.9958577 2.8400000
## [1] 0.9959159 2.8500000
## [1] 0.9959721 2.8600000
## [1] 0.9960265 2.8700000
## [1] 0.996079 2.880000
## [1] 0.9961297 2.8900000
## [1] 0.9961786 2.9000000
## [1] 0.9962258 2.9100000
## [1] 0.9962713 2.9200000
## [1] 0.9963153 2.9300000
## [1] 0.9963576 2.9400000
## [1] 0.9963983 2.9500000
## [1] 0.9964376 2.9600000
## [1] 0.9964754 2.9700000
## [1] 0.9965118 2.9800000
## [1] 0.9965468 2.9900000
## [1] 0.9965804 3.0000000
## [1] 0.9966128 3.0100000
## [1] 0.9966438 3.0200000
## [1] 0.9966736 3.0300000
## [1] 0.9967022 3.0400000
## [1] 0.9967296 3.0500000
## [1] 0.9967559 3.0600000
## [1] 0.996781 3.070000
## [1] 0.9968051 3.0800000
## [1] 0.9968281 3.0900000
## [1] 0.9968501 3.1000000
## [1] 0.9968711 3.1100000
## [1] 0.9968912 3.1200000
## [1] 0.9969103 3.1300000
## [1] 0.9969284 3.1400000
## [1] 0.9969457 3.1500000
## [1] 0.9969622 3.1600000
## [1] 0.9969778 3.1700000
## [1] 0.9969926 3.1800000
## [1] 0.9970066 3.1900000
## [1] 0.9970199 3.2000000
## [1] 0.9970324 3.2100000
## [1] 0.9970442 3.2200000
## [1] 0.9970553 3.2300000
## [1] 0.9970657 3.2400000
## [1] 0.9970755 3.2500000
## [1] 0.9970846 3.2600000
## [1] 0.9970931 3.2700000
## [1] 0.997101 3.280000
## [1] 0.9971084 3.2900000
## [1] 0.9971152 3.3000000
## [1] 0.9971214 3.3100000
## [1] 0.9971272 3.3200000
## [1] 0.9971324 3.3300000
## [1] 0.9971371 3.3400000
## [1] 0.9971413 3.3500000
## [1] 0.9971451 3.3600000
## [1] 0.9971485 3.3700000
## [1] 0.9971514 3.3800000
## [1] 0.9971539 3.3900000
## [1] 0.997156 3.400000
## [1] 0.9971577 3.4100000
## [1] 0.997159 3.420000
## [1] 0.99716 3.43000
## [1] 0.9971606 3.4400000
## [1] 0.9971609 3.4500000
## [1] 0.9971608 3.4600000
## [1] 0.9971605 3.4700000
## [1] 0.9971598 3.4800000
## [1] 0.9971589 3.4900000
## [1] 0.9971576 3.5000000
## [1] 0.9971561 3.5100000
## [1] 0.9971544 3.5200000
## [1] 0.9971523 3.5300000
## [1] 0.9971501 3.5400000
## [1] 0.9971476 3.5500000
## [1] 0.9971448 3.5600000
## [1] 0.9971419 3.5700000
## [1] 0.9971388 3.5800000
## [1] 0.9971354 3.5900000
## [1] 0.9971319 3.6000000
## [1] 0.9971282 3.6100000
## [1] 0.9971243 3.6200000
## [1] 0.9971202 3.6300000
## [1] 0.997116 3.640000
## [1] 0.9971116 3.6500000
## [1] 0.997107 3.660000
## [1] 0.9971024 3.6700000
## [1] 0.9970976 3.6800000
## [1] 0.9970926 3.6900000
## [1] 0.9970876 3.7000000
## [1] 0.9970824 3.7100000
## [1] 0.9970771 3.7200000
## [1] 0.9970717 3.7300000
## [1] 0.9970662 3.7400000
## [1] 0.9970606 3.7500000
## [1] 0.9970549 3.7600000
## [1] 0.9970491 3.7700000
## [1] 0.9970432 3.7800000
## [1] 0.9970373 3.7900000
## [1] 0.9970313 3.8000000
## [1] 0.9970252 3.8100000
## [1] 0.997019 3.820000
## [1] 0.9970128 3.8300000
## [1] 0.9970065 3.8400000
## [1] 0.9970002 3.8500000
## [1] 0.9969938 3.8600000
## [1] 0.9969874 3.8700000
## [1] 0.9969809 3.8800000
## [1] 0.9969744 3.8900000
## [1] 0.9969679 3.9000000
## [1] 0.9969613 3.9100000
## [1] 0.9969547 3.9200000
## [1] 0.996948 3.930000
## [1] 0.9969414 3.9400000
## [1] 0.9969347 3.9500000
## [1] 0.9969279 3.9600000
## [1] 0.9969212 3.9700000
## [1] 0.9969145 3.9800000
## [1] 0.9969077 3.9900000
erro<--prob+pnorm(seq(0,3.99,0.01))
b<-seq(0,3.99,0.01)
plot(b,erro,main="Gráfico erro -Verificar correção do gráfico-")

Note that the echo = TRUE parameter was added to the code chunk to printing of the R code that generated the plot.