HW 2
1. Let X1, . . . , Xn be a random sample from a Uniform (0, θ) distribution. (a) Find the CDF for Y(n) = max(X1,…,Xn).
(b) Show that (Y(n), Y(n)/α1/n) is a (1 − α)100% confidence interval for θ. 2. Suppose that X is exponentially distributed with mean θ.
(a) Show that 0, X is a 95% confidence interval for θ based on a single observation X. −ln(0.95)
Due: Feb 15, 2021. 23:59 pm.
Textbook 4.2.25, 4.2.26, 4.2.27, 4.4.5, 4.4.20.
X , ∞ is a 95% confidence interval for θ based on a single observation X. −ln(0.05)
(b) Show that
(c) Which confidence interval do you prefer? Why?
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