Exercícios propostos na última aula:

library(RcmdrMisc)

## Carregando pacotes exigidos: car

## Carregando pacotes exigidos: carData

## Carregando pacotes exigidos: sandwich

.x <- seq(-3.291, 3.291, length.out=1000)    
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0, 4)), col=c('#0080C0', '#BEBEBE'), legend=FALSE)

# P(0<X<0,11)

# P(0 < X < 0,11) = 0,04380
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0, 0.11)), 
          col=c('red'), legend=FALSE)

# P(-2,2<X<0,12)

# P (-2,2 < X < 0,12) = 053386
# P (-2,2 < X < 0,12) = P (-2,2 < X < 0) + P (0 < X < 0,12)
# P (-2,2 < X < 0,12) = P (0 < X < 2,2) + P (0 < X < 0,12)
#                       0,48610       +  0,04776 = 0,53386

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-2.2,0),c(0,0.12)), 
          col=c('green','blue'), legend=FALSE)

# P(-1<X<2,1)

# P(-1 < X < 2,1) =  0,82348
# P(-1 < X < 2,1) = P (-1 < X < 0) + P (0 < X < 2,1)
#                   P (0 < X < 1)   + P (0 < X < 2,1)
#                 =  0,34134     +0,48214 = 0,82348

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-1,0),c(0,2.1)), 
          col=c('green','purple'), legend=FALSE)

# P(0<X<1,83)

# P (0 < X < 1,83) = 
# P (0 < X < 1,83) = 0,46638
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0, 1.83)), 
          col=c('orange'), legend=FALSE)

# P(-0,87<X<1,54)

# P (-0,87 < X < 1,54) = 0,74607
# P (-0,87 < X < 1,54) = P (-0,87 < X < 0) + (0 < X < 1,54)
#                      = P (0 < X < 0,87) + (0 < X < 1,54)
#                      = 0,30785          + 0,43822 =  0,74607  
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-0.87,0),c(0,1.54)), 
          col=c('blue','yellow'), legend=FALSE)

# P(x>2,5)

# P (x > 2,5)= 0,5 - 0,49379 = 0,00621
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0,2.5),c(0,0.5)), 
          col=c('pink','brown'), legend=FALSE)

# P(x>-2)

# P (x > -2)= 0,5 + 0,47725 = 0,97725
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0,2),c(0,0.5)), 
          col=c('blue','brown'), legend=FALSE)

# P(X<0)

# P (x < 0) =  0,5
plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0,0.5)), 
          col=c('red'), legend=FALSE)

Exercícios de Distribuição Normal

Thiago Castro

26/01/2022

Exercícios propostos na última aula:

P(X=1,54)

P (X = 1,54)= 0