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Cagdas Ozgenc
Cagdas Ozgenc
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Suppose that $X_1, X_2, ... , X_n$ are mutually independent random variables. There is a random variable $C \sim Uniform(-1,1)$$C \sim U(-1,1)$, which all $X$s depend on. How can I construct such $X$s so that they are unconditionally independent with zero mean?

Suppose that $X_1, X_2, ... , X_n$ are mutually independent random variables. There is a random variable $C \sim Uniform(-1,1)$, which all $X$s depend on. How can I construct such $X$s so that they are unconditionally independent with zero mean?

Suppose that $X_1, X_2, ... , X_n$ are mutually independent random variables. There is a random variable $C \sim U(-1,1)$, which all $X$s depend on. How can I construct such $X$s so that they are unconditionally independent with zero mean?

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Cagdas Ozgenc
Cagdas Ozgenc
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  • 68

Series of mutually independent variables that are dependent on an auxiliary random variable

Suppose that $X_1, X_2, ... , X_n$ are mutually independent random variables. There is a random variable $C \sim Uniform(-1,1)$, which all $X$s depend on. How can I construct such $X$s so that they are unconditionally independent with zero mean?