Actividad 4.4.2

Problema 1

set.seed(404)
x = rnorm(300, mean=100, sd=15)
media_muestral = mean(x)
varianza_muestral = var(x)
error_estandar = sqrt(varianza_muestral/length(x))
lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 99.73881

varianza_muestral

## [1] 207.2106

c(lim_inf, lim_sup)

## [1]  98.07664 101.40098

Problema 2

set.seed(404)
x = runif(200, min = 0, max = 1)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 0.5300178

varianza_muestral

## [1] 0.08183999

c(lim_inf, lim_sup)

## [1] 0.4895604 0.5704751

Problema 3

set.seed(404)
x = rexp(400, rate = 2)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 0.4890831

varianza_muestral

## [1] 0.2505712

c(lim_inf, lim_sup)

## [1] 0.4390261 0.5391402

Problema 4

set.seed(404)
x = rbinom(500, size = 10, prob = 0.5)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 4.994

varianza_muestral

## [1] 2.354673

c(lim_inf, lim_sup)

## [1] 4.856751 5.131249

Problema 5

set.seed(404)
x = rpois(250, lambda = 4)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 4.168

varianza_muestral

## [1] 3.746763

c(lim_inf, lim_sup)

## [1] 3.923157 4.412843

Problema 6

set.seed(404)
x = rchisq(350, df = 5)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 5.159589

varianza_muestral

## [1] 10.15094

c(lim_inf, lim_sup)

## [1] 4.818986 5.500193

Problema 7

set.seed(404)
x = rt(400, df = 10)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 0.02933854

varianza_muestral

## [1] 1.168638

c(lim_inf, lim_sup)

## [1] -0.07876505  0.13744212

Problema 8

set.seed(404)
x = rf(200, df1 = 5, df2 = 10)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 1.265397

varianza_muestral

## [1] 1.361678

c(lim_inf, lim_sup)

## [1] 1.100371 1.430423

Problema 9

set.seed(404)
x = rbinom(300, size = 1, prob = 0.3)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 0.32

varianza_muestral

## [1] 0.2183278

c(lim_inf, lim_sup)

## [1] 0.266046 0.373954

Problema 10

set.seed(404)
x = rbeta(250, shape1 = 2, shape2 = 5)

media_muestral = mean(x)

varianza_muestral = var(x)

error_estandar = sqrt(varianza_muestral/length(x))

lim_inf = media_muestral-2*error_estandar
lim_sup = media_muestral+2*error_estandar

media_muestral

## [1] 0.2820332

varianza_muestral

## [1] 0.02240181

c(lim_inf, lim_sup)

## [1] 0.2631010 0.3009655