Consider the simple linear regression model Yi = βxi + εi, for i = 1, …, n; where E(εi) = 0, Cov(εi, εk) = 0 if i ≠ k and Var(εi) = xi2σ2. The best linear unbiased estimator of β is:

Let X1, X2, ... be a sequence of independent and identically distributed random variables having a Binomial(3, 14) distribution. For j = 1, 2, ..., define Yj = 1 if Xj ≤ √5, and Yj = 0 otherwise. If 1n ∑j=1n Yj2 converges almost surely to a constant c as n → ∞, then the value of c is:

Let X be a single sample from an absolutely continuous distribution with probability density function f(x|θ) = 2θ2 (θ - x) for 0 0 is unknown. Which of the following intervals is a 95% confidence interval for θ?