The maximum likelihood estimate of the rate parameter (λ) of an exponential population based on the sample 1, 3, 1, 8, 2, 8, 3, 8, 2, 13 is:

Let X1, X2, ..., Xn (n ≥ 2) be a random sample from a continuous distribution with the probability density function: f(x | θ) = (1/(2θ)) e-|x-θ|/θ, x ∈ R where θ (> 0) is an unknown parameter. Let Un = (1/n) ∑i=1n Xi, Vn = (1/n) ∑i=1n Xi2, and Sn2 = (1/(n-1)) ∑i=1n (Xi - Un)2. Then, which of the following statements is true?

Let X1, X2, ..., Xn be independent and identically distributed random variables with the probability density function: f(x | θ) = e-(x-θ) if x ≥ θ, and 0 otherwise where θ ∈ R is the unknown parameter. Let Y = min(X1, X2, ..., Xn). Which of the following is a confidence interval for θ with the confidence coefficient (1-α), where α ∈ (0, 1)?