server <- function(input, output) {

  rv <- reactiveValues(
    norm = rnorm(500),
    unif = runif(500),
    chisq = rchisq(500, 2))

  observeEvent(input$renorm, { rv$norm <- rnorm(500) })
  observeEvent(input$reunif, { rv$unif <- runif(500) })
  observeEvent(input$rechisq, { rv$chisq <- rchisq(500, 2) })

  output$norm <- renderPlot({
    hist(rv$norm, breaks = 30, col = "grey", border = "white",
      main = "500 random draws from a standard normal distribution")
  })
  output$unif <- renderPlot({
    hist(rv$unif, breaks = 30, col = "grey", border = "white",
      main = "500 random draws from a standard uniform distribution")
  })
  output$chisq <- renderPlot({
    hist(rv$chisq, breaks = 30, col = "grey", border = "white",
       main = "500 random draws from a Chi Square distribution with two degree of freedom")
  })
}

shinyApp(server = server, ui = ui)