題組內容

1. If X is a random variable with Pareto distribution, then the probability that X is greater than some number x, ie. the complementary CDF, is given by

, where x_m is the (necessarily positive) minimum possible value of X, and a is a positive parameter.

(d) Let X₁and X₂are independent identically distributed random variables with Pareto distribution with parameter x_m and a defined earlier. Show that the two random variables min{X₁,x₂} and (X₁+ X₂)/min{X₁, X₂} are independent. (10 points)

題組內容

(d) Let X₁and X₂are independent identically distributed random variables with Pareto distribution with parameter x_m and a defined earlier. Show that the two random variables min{X₁,x₂} and (X₁+ X₂)/min{X₁, X₂} are independent. (10 points)

相關申論題

相關試卷

題組內容

(d) Let X1 and X2 are independent identically distributed random variables with Pareto distribution with parameter xm and a defined earlier. Show that the two random variables min{X1,x2} and (X1+ X2)/min{X1, X2} are independent. (10 points)

相關申論題

相關試卷

(d) Let X₁and X₂are independent identically distributed random variables with Pareto distribution with parameter x_m and a defined earlier. Show that the two random variables min{X₁,x₂} and (X₁+ X₂)/min{X₁, X₂} are independent. (10 points)