ind 1. Let X₁, X2, ..., Xn Fx, where Fx is the cumulative distribution function. In Home- work 1, you proved that Fx(X;) is uniformly distributed between [0, 1]. Here we con- sider a different problem. Suppose that we order these n random variables to obtain X(1) ≤ X(2), ….. ≤ X(n). We also define Y₁ = Fx(X()). What is the joint probability density function of Y₁, Y2,..., Yn?

MATLAB: An Introduction with Applications
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1. Let X₁, X2,..., Xn Fx, where Fx is the cumulative distribution function. In Home-
work 1, you proved that Fx (X;) is uniformly distributed between [0, 1]. Here we con-
sider a different problem. Suppose that we order these n random variables to obtain
X(1) ≤ X(2),... ≤X(n). We also define Y; = Fx(X(i)). What is the joint probability
density function of Y₁, Y2,..., Yn?
Transcribed Image Text:iid 1. Let X₁, X2,..., Xn Fx, where Fx is the cumulative distribution function. In Home- work 1, you proved that Fx (X;) is uniformly distributed between [0, 1]. Here we con- sider a different problem. Suppose that we order these n random variables to obtain X(1) ≤ X(2),... ≤X(n). We also define Y; = Fx(X(i)). What is the joint probability density function of Y₁, Y2,..., Yn?
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