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Correlation Between the Minimum and Maximum — MeetProba

Exercises/Continuous Distributions

Correlation Between the Minimum and Maximum

Correlation Between the Minimum and Maximum

Medium

Exercise 4 / 9

Answer

Let $X_1, X_2, \dots, X_n$ be i.i.d. random variables with a Uniform distribution on $[0,1]$ . Define:

Y_n = \min(X_1, X_2, \dots, X_n), \quad Z_n = \max(X_1, X_2, \dots, X_n)

Question: Compute $\text{Corr}(Y_n, Z_n)$ .

2

,

…

,

Xn

)

,

Zn

=

max(X1,X2,…,Xn)