f = function(x)
{
if( (0 <= x) & (x<= 7) )
{
return(1/7)
}
else
{
return(0)
}
}
f(10)
f(6)
1/7
integrate(f)
f
integrate(f)
integrate(0)
integrate(1/7)
f
integrate(f)
integrate(f, lower = inf)
integrate(f, lower = infinte)
infinite
inf
infy
infty
Inf
integrate(f, lower = Inf)
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
if( (0 >= x) & (x<= 7) )
{
return(1/7)
}
else
{
return(0)
}
}
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
if( (0 >= x) & (x<= 7) )
{
return(1/7)
}
else
{
return(0)
}
}
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
if( (x >= 0) & (x<= 7) )
{
return(1/7)
}
else
{
return(0)
}
}
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
if( (x >= 0) & (x<= 7) )
{
return(1/7)
}
else
{
return(0)
}
}
integrate(f)
f = function(x)
{
(x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
}
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
if( (x >= 0) & (x<= 7) )
{
1/7
}
else
{
0
}
}
#f = function(x)
#{
#  (x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
#}
integrate(f, lower = Inf, upper = Inf)
f = function(x)
{
(x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
}
integrate(f)
f = function(x)
{
(x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
}
integrate(f, lower = Inf, upper = Inf)
f
plot(f)
library(distr6)
install.packages(distr6)
install.packages("distr6")
library(distr6)
?distr6::kthmoment()
distr6::kthmoment(f, 1)
library(distr6)
f = function(x)
{
(x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
}
integrate(f, lower = Inf, upper = Inf)
plot(f)
distr6::kthmoment(f, 1)
distr6::mgf(f,1)
library(distr6)
f = function(x)
{
(x<0)*0 + (x>=0 & x<=7) * (1/7) + (x>7)*0
}
integrate(f, lower = Inf, upper = Inf)
plot(f)
distr6::mgf(f)
?mgf
distr6::mgf(f,1)
mfg(1)
mgf(1)
mean(f)
integrate(f, lower = Inf, upper = Inf)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
mean(x1)
?distr6::Uniform
?distr6::Uniform$new(lower = 0 , upper = 1/7)
distr6::Uniform$new(lower = 0 , upper = 1)
ok = distr6::Uniform$new(lower = 0 , upper = 1/7)
ok$mgf()
ok$mgf
ok
plot(ok)
?dunif
ok = distr6::Uniform$new(f, lower = 0 , upper = 1/7)
?distr6::Distribution
lenght(1)
length(1)
length(3)
ok = distr6::Uniform$new(f, lower = 0 , upper = 1/7)
?distr6::Uniform$new()
?distr6::Uniform
distr6::Uniform$new(lower = 0 , upper = 1/7)
ok
plot(ok)
ok$mgf
ok$mgf(t = 1)
distr6::Uniform$new(lower = 0 , upper = 7)
d = distr6::Uniform$new(lower = 0 , upper = 7)
plot(d)
d$mean()
d = distr6::Uniform$new(lower = 0 , upper = 7)
integrate(d)
d
d$pdf()
d$print()
d$summary()
d$mgf(1)
d = distr6::Uniform$new(lower = 0 , upper = 7)
plot(d)
d$mgf(t = 1)
integrate(d)
d$cdf()
d$cdf
d$pdf
integrate(d$pdf)
integrate(d$pdf, lower = 0 , upper = 7)
integrate(d$pdf, lower = -Inf , upper = Inf)
d$mgf(t = 1)
as.matrix(x1,x2,x3)
x2
x3
as.matrix(x1,x2,x3)
x1
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
as.matrix(x1,x2,x3)
matrix(x1,x2,x3)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
matrix(x1,x2,x3)
?matrix
?as.matrix
c(x1,x2,x3)
as.matrix(c(x1,x2,x3))
as.matrix(c(x1,x2,x3), nrow(3))
as.matrix(c(x1,x2,x3), nrow= 3)
matrix(c(x1,x2,x3), nrow= 3)
matrix(c(x1,x2,x3), nrow= 4)
matrix(c(x1,x2,x3), nrow= 4)
matrix(c(x1,x2,x3), ncol = 4)
matrix(c(x1,x2,x3), ncol = 3)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
matrix(c(x1,x2,x3), ncol = 3)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
m = matrix(c(x1,x2,x3), ncol = 3)
m
Matrix::mean(m)
cov(m)
cov(m)
mean(m)
cov(x1,x2,x3)
mean(x1)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
m = matrix(c(x1,x2,x3), ncol = 3)
vector_mean = c(mean(x1), mean(x2), mean(x3))
cov(m)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
m = matrix(c(x1,x2,x3), ncol = 3)
vector_mean = c(mean(x1), mean(x2), mean(x3))
cov(m)
vector_mean
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
m = matrix(c(x1,x2,x3), ncol = 3)
vector_means = c(mean(x1), mean(x2), mean(x3))
cov(m)
x1 = c(12,11,8,14,10)
x2 = c(10,8,5,11,7)
x3= c(8,11,11,13,6)
m = matrix(c(x1,x2,x3), ncol = 3)
vector_means = c(mean(x1), mean(x2), mean(x3))
vector_means
cov(m)
plot(d)
library(distr6)
d = distr6::Uniform$new(lower = 0 , upper = 7)
#(i)
integrate(d$pdf, lower = -Inf , upper = Inf)
#(ii)
plot(d)
curve(d)
curve(d)
#(ii)
plot(d)
?curve()
curve(d,from = 0, to=7)
curve(plot(d),from = 0, to=7)
curve(from = 0, to=7)
#(ii)
curve(d)
plot(d)
curve(d$pdf)
plot(d$pdf)
plot(d$cdf())
plot(d$cdf
)
plot(d)
curve(d)
curve(distr6::Uniform$new(lower = 0 , upper = 7))
curve(distr6::Uniform$new(lower = 0 , upper = 7))
curve(d(x))
d$print()
d$print
d$summary()
curve(d$summary())
plot(d, type='l')
plot(d)
plot(d)[1]
curve(d)
d
d$cdf()
d$cdf
d$pdf
curve(d$pdf)
curve(d$pdf(x))
curve(d(x))
#(i)
integrate(d$pdf, lower = -Inf , upper = Inf)