Question

5 Random Numbers and Histograms [Applied] Let x = x1 + ... + x20, the sum of 20 independent Uniform(0,1) random variables. In R, create 1,000 simulations of x and plot their histogram. On the histogram, overlay a graph of the normal density function with the same mean as x. Comment on any differences between the histogram and the curve. Hint 1: To plot a histogram in R you can build on the following code: library(ggplot2) df <- data.frame( x = rnorm rm (1000) ) ggplot(df, aes(x)) + geom_histogram(aes (y=..density..)) Hint 2: In ggplot you cannot plot the normal density as a function. But you can easily simulate lots of values drawn from a normal distribution (say 1,000) and plot these data as a geom_density(). The main challenge for you to figure out is how to use two ggplot layers, each with its own data.frame: The first layer uses the data from x the second uses data from the normal distribution.

Answer 1

R Code:

library(ggplot2)

dataframe <- data.frame(x = rnorm(1000))

ggplot(dataframe, aes(x=x)) +
    geom_histogram(aes(y = ..density..), binwidth=0.3) +
    geom_density(fill="blue", alpha = 0.2)

Output:

Answer 2

solution:

given data:

R code:

# creating the 1000 random variable
x=c()
for(i in 1:1000){
x[i]=sum(runif(20,0,1))
}
hist(x)

mu=mean(x)
#creating 1000 normal random variable
b=rnorm(1000,mean(x),sd(x))
b

hist(x)
par(new=T)
plot(density(b))

#comment we find that both are them are following the same distribuiton

please give me thumb up