Bunny Weights

Nagesh
Jun 19, 2015

Central Limit Theorem

  • The Central Limit Theorem states that
    • The distribution of averages of IID variables becomes that of a standard normal as the size increases.
  • Examples
    • Inter-arrival time of births
    • Means of roll of fair die roll
    • Means of height of some defined population (men, women, etc.)
    • More

Bunny weight example

  • We want to find the mean weight of bunnies
  • We cannot weigh every single bunny to calculate the mean
  • So, we use CLT
    • Take a sample of bunnies whose size is k
    • Calculate its mean, μ
    • Repeat previous steps for n number of times
    • As n increases, we will see the distribution of mean to approach that of normal distribution

Sample plot - Histogram

  • Histogram with k=10 and n=20 plot of chunk unnamed-chunk-1
  • Histogram with k=10 and n=50 plot of chunk unnamed-chunk-2

Sample plot - Normal Distribution curve

  • Plot with k=10 and n=1000 (μ=3.5)

plot of chunk unnamed-chunk-3

Conclusion

  • The Central Limit Theorem has been proved by
    • increasing size of samples
    • increasing number of samples
    • showing the distribution to be close to normal distribution