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-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-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-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.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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