मान लीजिए X = (X1, X2)T एक द्विचर प्रसामान्य बंटन (bivariate normal distribution) का पालन करता है जिसका माध्य सदिश (0, 0)T और सहप्रसरण आव्यूह Σ इस प्रकार है: Σ = ⌈ 5 -3 ⌉ ⌊ -3 10 ⌋ Y = (X1, 5 − 2X2)T का माध्य सदिश और सहप्रसरण आव्यूह हैं:

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?