An example of a shiny App that can be run from a Gist

server.R

library(shiny)

# Define server logic required to draw a histogram
shinyServer(function(input, output) {

    mysamples <- reactive({
        fdist <- switch(input$dist,
                        Normal = rnorm,
                        Exponential = rexp,
                        Poisson = function(n) rpois(n,4))
        replicate(input$p, fdist(input$n))
    })
    
    output$thehist <- renderPlot({
        hist(colMeans(mysamples()),
             col = "blue")
    })

})

ui.R

library(shiny)

# Define UI for application that draws a histogram
fluidPage(

    # Application title
    titlePanel("Central Limit Theorem"),

    # Sidebar with a slider input for number of bins
    sidebarLayout(
        sidebarPanel(
            sliderInput("n",
                        "Number of observations:",
                        min = 5,
                        max = 50,
                        value = 30),
            sliderInput("p",
                        "Number of samples",
                        min = 20, max = 1000,
                        value = 500),
            selectInput("dist",
                        "Select a distribution",
                        choices = c("Normal","Exponential",
                                    "Poisson"))
            
        ),

        # Show a plot of the generated distribution
        mainPanel(
            plotOutput("thehist")
        )
    )
)