## In this lab we'll rehearse our understanding of the sampling distribution.
## 1. Plot the probability density function for the Exponential(beta =
## 2) distribution and descirbe the shape of this distribution. Note
## that in R's help files, beta is referred to as the rate parameter
## (and is called lambda).
## 2. Generate N = 10 observations from the Exponential(beta = 2)
## distribution.
## 2. Calculate the mean of the vector of data generated in 2.
## 3. Repeat steps 2. - 3. R = 999 times. Don't forget to
## pre-allocate. Plot, appropriately, the R sample means.
## 4. Describe the shape of the sampling distribution for the mean.
## 5. Increase the sample size to N = 100. Describe how the sampling
## distribution changes.
## 6. Increase the sample size to N = 1001. Describe how the sampling
## distribution changes.
## 7. Plot the probability density function for the gamma( alpha = 40,
## beta = 2) distribution and descirbe the shape of this distribution.
## Note that in R's help files, alpha is referred to as the shape
## parameter and beta is referred to as the rate parameter.
## 8. Generate N = 10 observations from the Gamma(alpha = 40, beta = 2)
## distribution.
## 9. Estimate the parameters alpha and beta using the likelihood
## method from the data generated in 8.
## 10. Repeat steps 8. - 9. R = 999 times. Don't forget to
## pre-allocate for each parameter. Make one plot for each parameter
## based on the R estimates.
## 11. Describe the shape of the sampling distributions.
## 12. Increase the sample size to N = 100. Describe how the sampling
## distribution changes.
## 13. Increase the sample size to N = 1001. Describe how the sampling
## distribution changes.
## 14. Which seems to have a bigger effect on the shape of the
## sampling distribution, the sample size N or the shape of the
## population distribution?