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#                       AULA 9 - PRATICA DE R E PYTHON                       #
#                                                                            #
# SME0320 Prof. Jorge Luis Bazán                                             #
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rm(list = ls()); cat('\014')


##############################################################################
# VAMOS PRATICAR #
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# Gerando uma amostra da distribui??o Normal Padr?o
set.seed(123) 
y = rnorm(1000, mean = 0, sd = 1)
head(y, 20)

# Alterando m?dia e desvio padr?o
set.seed(321) 
y2 = rnorm(1000, 3, 2)
head(y2)


# Histograma da Normal(0,1) 
x11()
hist(y, prob = TRUE, main = "Histograma de y")


# Adicionando curva densidade
curve(dnorm(x), add = T, col = "blue", lwd = 2)


# Curvas da Normal com diferentes m?dias
x11()
curve(dnorm(x), xlim = c(-6, 6), ylim = c(0, 0.5), lwd = 2)
curve(dnorm(x, -2), col = "red", lwd = 2, add = TRUE)
curve(dnorm(x, 2), col = "blue", lwd = 2, add = TRUE)
legend(x = "topleft",
       legend = c("N(0,1)", "N(-2,1)", "N(2,1)"),
       col = c("black", "red", "blue"), 
       lwd = 2, cex = 1.5)


# Curvas da Normal com diferentes desvio padr?o
curve(dnorm(x), xlim = c(-5, 5), ylim = c(0, 0.8), lwd = 2)
curve(dnorm(x, sd = 2), col = "red", lwd = 2, add = TRUE)
curve(dnorm(x, 0, 0.5), col = "blue", lwd = 2, add = TRUE)
legend(x = "topright",
       legend = c("N(0,1)", "N(0,2)", "N(0, 0.5)"),
       col = c("black", "red", "blue"), 
       lwd = 2, cex = 1.5)


# Medidas descritivas
summary(y)


install.packages("psych", dep = T)
library(psych)
describe(y)



##############################################################################
# EXERC?CIO 1 #
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# X ? uma v.a com distribui??o Normal de m?dia = 24 e desvio padr?o = 3.8
# X = {tempo de viagem at? o trabalho}

mu = 24; sigma = 3.8


#######################
### ALTERNATIVA (a) ### 
# P(X > 15) = ?

x = 15

z = round((x - mu) / sigma, 2)
z

Pz = 1 - pnorm(z) 
round(Pz, 4)

Pz = pnorm(z, lower.tail = F) 
round(Pz, 4)


# Ou podemos resolver da seguinte forma

Px = 1 - pnorm(x, 24, 3.8) 
round(Px, 4)


Px = pnorm(x, mu, sigma, lower.tail = F)
round(Px, 4)



#######################
### ALTERNATIVA (b) ###
# sigma = ?

sigma1 = (26 - mu)/round(qnorm(0.85), 2)
round(sigma1, 2)


#######################
### ALTERNATIVA (c) ###
# X = ? 

x1 = round(qnorm(0.80), 2)*sigma + mu
x1


#######################
### ALTERNATIVA (d) ###

# Y = {numero de viagens pelo menos 30 minutos}
# Y ~ binomial(n = 3, p = ?)
# p = P(X >= 30) 

x = 30
p = round(pnorm(x, 24, 3.8, lower.tail = F), 4)
p

# P(Y = 2) = ?
n = 3; y = 2
Py = dbinom(y, 3, p) 
round(Py, 4)