1. This question uses the data in the whales.csv file. The data represent the time in hours recorded for a sample of bowhead whales to swim 1km as part of a study to understand the whale population. (a) (5 points) Make a histogram and Q-Q plot of the data. Is a normal distribution a plausible fit for this data? Is a gamma distribution plausible? Justify your answer. (b) (5 points) Estimate the parameters for a gamma distribution using method of moments. (c) (5 points) Estimate the parameters for a gamma distribution using maximum likelihood using the fitdistrcommand in the MASS package (You will have to first install.packages("MASS"), then library(MASS) to use the fitdistrfunction). d) (5 points) Plot the estimated gamma densities on top of the histogram (plot the histogram with freq=F, then use the lines() command to overlay the gamma distributions). Which fit do you think is more representative of the sample and why? (e) (5 points) Estimate the sampling distribution and standard errors for the parameters estimated by the MLE using the bootstrap. Plot a histogram of your estimated sampling distributions. (f) (5 points) Find 95% t-confidence intervals for both parameters using the estimated standard errors from the bootstrap as well a 95% bootstrap percentile confidence interval for each of the MLEs. Would one interval be better to use? Why? 2. Let Xo, .., X be a random sample from the exponential distribution with pdf f ( x) = -0 6, 0