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Let Y1, Y2,…, Yn denote independent and identically distributed random variables from a power family distribution with parameters α and θ = 3. Then, as in Exercise 9.43, if α > 0,
Show that E(Y1) = 3α/(α + 1) and derive the method-of-moments estimator for α.
9.43 Let Y1, Y2,…, Yn denote independent and identically distributed random variables from a power family distribution with parameters α and θ. Then, by the result in Exercise 6.17, if α, θ > 0,
If θ is known, show that
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Mathematical Statistics with Applications
- Let X1, . . . , Xn be independent random variables, such that Xi ∼ Exponential(θ), for i =1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.arrow_forwardSuppose that the random variables X1,...,Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1,. . .,Xn}, and let Yn = max{X1,...,Xn}. Find E(Y1) and E(Yn).arrow_forward
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