虽然我能够生成正确数量的样本，并且这些样本的大小都是正确的，但每个样本都完全相同。
目前，我正在尝试创建一个演示中心极限定理的应用程序，特别是针对样本均值分布的情况。当我意识到直方图在x轴上具有相同的精确值时，我希望应用程序生成正确的采样分布，这表明每个样本的均值完全相同。
根据我自己的测试，我认为问题出在sample_i（）React表达式上，因为后面的React表达式工作得很好。
我是否必须实现另一个React式表达式才能解决这个问题？

library(shiny)

ui <- fluidPage(
  titlePanel("Demonstration of the Central Limit Theorem"),
  fluidRow(
    column(4, selectInput("dist", "Distribution",
                          c("Normal", "Uniform", "Poisson", "Binomial"))),
    column(4, numericInput("n_sample", "Number of samples", value = 50)),
    column(4, numericInput("size", "Sample size", value = 100))
  ), 
  tabsetPanel(
    id = "params",
    type = "hidden",
    tabPanel("Normal",
             numericInput("mean", "Mean", value = 0),
             numericInput("sd", "SD", value = 1)
    ),
    tabPanel("Uniform",
             numericInput("min", "Min", value = 0),
             numericInput("max", "Max", value = 1)
    ),
    tabPanel("Poisson",
             numericInput("r", "Rate", value = 1)
    ),
    tabPanel("Binomial",
             numericInput("p", "Probability of success", value = 0.5),
             numericInput("n", "Number of trials", value = 10)
    )
  ),
  plotOutput("hist"),
  verbatimTextOutput("length")
)

server <- function(input, output, session) {
  observeEvent(input$dist, {
    updateTabsetPanel(inputId = "params", selected = input$dist)
  })
  
  sample_i <- reactive({
    switch(input$dist, 
      Normal = rnorm(input$size, input$mean, input$sd),
      Uniform = runif(input$size, input$min, input$max), 
      Poisson = rpois(input$size, input$r), 
      Binomial = rbinom(input$size, input$n, input$p))
  })
  sample_dist <- reactive({
    replicate(n = input$n_sample, sample_i())
  })
  sample_dist_mean <- reactive({
      apply(sample_dist(), MARGIN = 2, mean) |>
        unlist() |> 
        as.numeric()
  })
  
  output$hist <- renderPlot(hist(sample_dist_mean()))
  output$length <- renderPrint(head(sample_dist(), n = 5))
}

shinyApp(ui, server)

请注意，当样本数设置为12时，控制台生成以下输出（通过输出的长度组件完成）。

[,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,]  0.5953571  0.5953571  0.5953571  0.5953571  0.5953571  0.5953571
[2,]  0.8323953  0.8323953  0.8323953  0.8323953  0.8323953  0.8323953
[3,] -1.0366900 -1.0366900 -1.0366900 -1.0366900 -1.0366900 -1.0366900
[4,]  2.1517537  2.1517537  2.1517537  2.1517537  2.1517537  2.1517537
[5,] -1.2565259 -1.2565259 -1.2565259 -1.2565259 -1.2565259 -1.2565259
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.5953571  0.5953571  0.5953571  0.5953571  0.5953571  0.5953571
[2,]  0.8323953  0.8323953  0.8323953  0.8323953  0.8323953  0.8323953
[3,] -1.0366900 -1.0366900 -1.0366900 -1.0366900 -1.0366900 -1.0366900
[4,]  2.1517537  2.1517537  2.1517537  2.1517537  2.1517537  2.1517537
[5,] -1.2565259 -1.2565259 -1.2565259 -1.2565259 -1.2565259 -1.2565259