Question

Suppose we are analyzing data from the exponential distribution, which has density function f (y) = ò exp (-5y) for y > 0, depending on a single parameter δ > 0, The exponential distribution arises in reliability theory as the waiting time until failure of a system that is subject to a constant risk of failure δ. (a) Using a computer: plot f(y; δ) as a function of y when δ-1. What is the area under this curve, and why? (b) How would you find P(Y>y) for the exponential distribution in general? (A brief mathematical expression will suffice.) (c) Plot f(y; δ) as a function of δ when y 1·This is the likelihood of δ when y = 1, it tells us how likely a failure after one time unit is at various levels of risk. Notice that this likelihood reaches a maximum at δ = 1. (d) Find the theoretical mean and variance of a single random variable following this exponential distribution

Answer 1

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