The Weibull distribution can be used to model time-to-failure in which the failure rate is proportional...

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The Weibull distribution can be used to model "time-to-failure" in which the failure rate is proportional to a power of time survived. A random variable has a Weibull distribution with parameters A and k if its probability density function is: for r >0 f(x; A, k) otherwise Suppose that you have a random sample of size n from a Weibull distribution distribution, X1,..., Xn, and that k is known. a) (2pts) Write down the likelihood function of A. b) (3pts) Find the maximum likelihood estimator of A. The Weibull distribution can be used to model "time-to-failure" in which the failure rate is proportional to a power of time survived. A random variable has a Weibull distribution with parameters A and k if its probability density function is: for r >0 f(x; A, k) otherwise Suppose that you have a random sample of size n from a Weibull distribution distribution, X1,..., Xn, and that k is known. a) (2pts) Write down the likelihood function of A. b) (3pts) Find the maximum likelihood estimator of A.

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