2. (R) The daily new COVID-19 cases were surging in Victoria since last Christmas. Let X be a random variable representing the number of new COVID-19 cases reported in Victoria. The following are 16 observations of X (from December 25, 2021 to January 9, 2022): 2108, 1608, 1999, 2738, 3767, 5137, 5919, 7442, 7172, 8577, 14020, 17636, 21997, 21728, 51356, 44155 (a) Give basic summary statistics for these data and produce a box plot. Briefly comment on center, spread and shape of the distribution. (b) Assuming a Log-normal distribution (LN(µ, σ) as in Question 1), compute maximum likelihood estimates for the parameters. (c) Draw a density histogram and superimpose a pdf for a Log-normal distribution using the estimated parameters. (d) Draw a QQ plot to compare the data against the fitted Log-normal distribution. Include a reference line. Comment on the fit of the model to the data. Hint: Quantile for the Log-normal distribution may be computed using the qlnorm function in R.
2. (R) The daily new COVID-19 cases were surging in Victoria since last Christmas. Let
X be a random variable representing the number of new COVID-19 cases reported in
Victoria. The following are 16 observations of X (from December 25, 2021 to January
9, 2022):
2108, 1608, 1999, 2738, 3767, 5137, 5919, 7442,
7172, 8577, 14020, 17636, 21997, 21728, 51356, 44155
(a) Give basic summary statistics for these data and produce a box plot. Briefly
comment on center, spread and shape of the distribution.
(b) Assuming a Log-
(c) Draw a density histogram and superimpose a
using the estimated parameters.
(d) Draw a QQ plot to compare the data against the fitted Log-normal distribution.
Include a reference line. Comment on the fit of the model to the data. Hint: Quantile for the Log-normal distribution may be computed using the qlnorm
in R.
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