Question 2: [9 points] Suppose the survival time X (in weeks) of a randomly selected male mouse exposed to 240 rads of Gamma radiation has a gamma distribution with parameters α = 8 and ẞ = 15. The probability density function of random variable X is given by α- 1 fx(x) = exp(-x/ẞ), x≥0, Bar(α) whose mean and the standard deviation are given by μx = aẞ and σx = ẞ√a, respectively. (a) Approximate the probability that a mouse survives between 60 and 120 weeks. [1] Data reported in "Survival Distributions: Reliability Applications in the Biomedical Services" by A. J. Gross and V. Clark suggests α=8.5 and ẞ 13.3, which were obtained using the 20 survival time data values summarized below: 152, 115, 109, 94, 88, 137, 152, 77, 160, 165, 125, 40, 128, 123, 136, 101, 62, 153, 83, 69 (b) Devise moment estimators for parameters α and ẞ, and subsequently find the moment estimates for these two parameters using the survival time data reported above. Compare these estimates from the values suggested by Gross and Clark, and state a reason for their discrepancy. [3] (c) Devise maximum likelihood estimators for the parameters α and ẞ and compare your results with those obtained from part (b). Which estimators would you recommend? Explain your answer. [5]