Given a covariate z, suppose that the log survival time y follows a linear model with a logistic error distribution, that is, y = ln(x) = μ + βζ + σ w where the pdf of w is given by eu f(w) = (1 + ewy, (a) for an individual with covariate z, find the conditional survival function of the survival time x, given z, namely, s(x |z). (b) the odds that an individual will die prior to time x is expressed by 1- sa lz)l/s(a |z). compute the odds of death prior to time x for this model. (c) consider two individuals with different covariate values. show that, for any time x, the ratio of their odds of death is independent of x. the log logistic regression model is the only model with this property

An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 120 lb and 161 lb. the new population of pilots has normally distributed weights with a mean of 125 lb and a standard deviation of 28.1 lb. a)if a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb.the probability is approximately? b. if 36 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 161 lb. the probability is approximately? c. when redesigning the ejection seat, which probability is more relevant? . part (b) because the seat performance for a single pilot is more important. b. part (b) because the seat performance for a sample of pilots is more important. c. part (a) because the seat performance for a sample of pilots is more important. d. part (a) because the seat performance for a single pilot is more important.