(ii) the failure rate function of a random variable denoting lifetime of a component. Establish the relation between them, if any. Prove that if h(t) is the failure rate function, then \int_0^\infty h(t) dt = \infty.

2Medium15 marks

A simple random sample of n clusters, each containing M elements, is drawn from the N clusters of the population and the clusters sampled are enumerated completely. Suggest an unbiased estimator of the population mean per element and derive the expression for the variance of the proposed estimator in terms of the population intraclass correlation coefficient.

3Medium8 marks

Let y_1, y_2, ... y_n be a random sample from N(\mu, \sigma^2) where \mu and \sigma^2 are both unknown. Obtain a confidence interval for \mu with confidence coefficient (1 - \alpha).

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