Data transformation and summarisation. An environmental engineer monitors daily rainfall (mm) over a 40-day period during the monsoon season. The data are heavily right-skewed: `0.5, 1.2, 0.0, 0.4, 0.8, 10.1, 12.5, 8.7, 5.3, 1.6, 0.0, 2.4, 3.5, 15.2, 20.0, 9.8, 4.6, 1.9, 0.0, 0.3, 0.2, 7.5, 6.2, 11.4, 13.0, 8.1, 2.2, 0.6, 0.0, 4.1, 5.9, 17.4, 18.3, 6.8, 3.1, 0.7, 0.0, 16.5, 9.0, 2.8`. (a) Compute the mean, median and standard deviation of the rainfall amounts. Comment on the effect of skewness on these measures. (b) Apply a logarithmic transformation to the rainfall data (use (log_{10}(x + 1)) to avoid log of zero). Recalculate the mean and standard deviation. Discuss whether the transformed data appear more symmetric. (c) Construct stem-and-leaf plots for the original and transformed data. Compare the shapes of the distributions and explain why transformations are useful in data analysis. (d) If rainfall depths follow a gamma distribution, outline the steps required to estimate the distribution's shape and scale parameters using the sample mean and variance. Explain how these parameters could be used to estimate the probability of daily rainfall exceeding 15 mm