Developing Data Products

Final Project - Coursera

This project will use Shiny application and Plotly package to simulate Flipping Coin event

• Part 1: Flipping 1 coin for t tossing times, then examine the probability of a Heads
• Part 2: Flipping n coins repeatedly t times, then examine and compare the Expectation and Variance from the simulator data with theoretical formular

Using rbinom to generate Heads or Tails of flipping 1 coin for t times and probability of Head is prob.
Note: data are generated from 1 to t for the ploting purpose

• For example: t= 40, prob= 0.5

    prob=0.5
    t=40
    data=data.frame(iter=0,probH=0)
    for(i in c(1:t)){
      sim=rbinom(i,1,prob)
      data[i,]=c(i,sum(sim)/i)}
    names(data)=c("flips","probHead")
    t(format(data[1:5,],digits=3))

         1       2       3       4       5      
flips    "1"     "2"     "3"     "4"     "5"    
probHead "0.000" "0.000" "0.667" "0.250" "0.200"

Similarly, using rbinom to simulate flipping n for t times and probability of heads is prob
For this part, the sample mean and variance, also theory expectation and variance will be generated

For example: t=15, prob=0.5, n=1:100
Note that 100 coins are generated for the purpose of ploting

  coins  mean sample var expectation theory var
1     1 0.667      0.238         0.5          0
2     2 0.867      0.267         1.0          0
3     3 1.600      0.829         1.5          1
4     4 2.133      0.838         2.0          1
5     5 3.067      0.781         2.5          1

Outputs produced by Shiny include:

• Part 1: Plot of probability of Heads vs number of flipping times
• Part 2: Plot of number of Heads from flipping 1 to 100 coins repeatedly t times
  and
  Table of Expectation and Variance for a specific number of coins

The application can be found at: https://zoeyle3294.shinyapps.io/Develop_Data_Products_final/

server.R and ui.R can be found at: https://github.com/ZoeyLe3294/Develop-Data-Product