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The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...

The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint: start with a confidence interval for μ)

f(x)=αβX^β-1 exp(-αX^β)

a. Derive 92% large sample confidence interval for α.

b. Find the maximum likelihood estimator of α.

Solutions

Expert Solution

Solution:-

Given that

The probability density function of lifespan of system component is given by

Here,

which is the pdf of exponential Distribution.

a) Derive 92% large sample confidence interval for .

92% confidence Interval for is

Let

Let and be the th percentile and 51 th percentile.

Then

The 92% confidence Interval is

b) Find the maximum likelihood estimator of .

MLE of is

likelihood function is given by

Log likelihood function is given by

Differentiating w.r.t we have,

MLE

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orchestra answered 1 year ago

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