Exponential Distribution - Simulation and MLEs
Exponential Distribution - Simulation and MLEs
This exercise involves using the command `set.seed(2021)` to initialize the random number generator in R before executing any R code. The first part requires generating a sample of size 180 from an Exponential distribution with parameter λ = 5 and calculating the sample median. Additionally, the median of the Exponential distribution is calculated to compare with the sample median, followed by commenting on the results.
Next, the maximum likelihood estimator (MLE) for λ is used to estimate the parameter based on the sample generated. This involves calculating λ using the sample mean. Subsequently, another sample of size 180 is generated from the Exponential distribution with the same parameter, and the MLE is used again to estimate the parameter λ.
Finally, the exercise involves comparing the estimated values of λ from both samples and commenting on any differences or similarities observed. This comprehensive approach helps in understanding the behavior of the Exponential distribution and the application of maximum likelihood estimation in statistical analysis.
CS1B - Paper I - Question 2