1. A software engineer is investigating the installation time of a new update. The update begins with an initial set-up time that lasts exactly seconds, followed by a dynamic sequence of operations that may take up to a further 7 seconds to complete. In other words, the overall installation time can be represented by a random variable X that takes some value on the interval [0,0+7] for some parameter >0 that is of interest for statistical inference. From the structure of the code, the engineer is able to deduce that: E[X] = 90+1 2 and Var(X)= 49 (0+1)2 Construct the methods of moments estimator T for 0, and prove that it is consistent. The software engineer decided to conduct an experiment by monitoring the time taken to install the software on 100 randomly chosen computers. From this experiment, the average installation time was 10.7 seconds. Compute the method of moments estimate t and show that the 95% confidence interval for 0 is (2.17, 2.36) seconds (to 2 d.p.).