Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x;...

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Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x;...

Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x; θ) = θ(1 − θ) x−1 for x = 1, 2, ... and 0 < θ < 1. Suppose that after taking the observations we find that ¯x = 5. 8.

a) Find the maximum likelihood estimator ˆθ of θ.

b) Find E[X¯] and var(X¯).

c) Use part (b) above together with the CLT and delta method to find the limiting distribution of √ n( ˆθ − θ).

d) Use part (c) to compute a 95 percent confidence interval for θ using the data that were obtained

solve only d please

math Statistics-And-Probability

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Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x;...

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