Suppose that (X ) is a continuous random variable that takes on real values and has characteristic function ( psi(t) exp ( t ) ) Use Theorem 2 28 to find the density of (X ) Theorem 2 28 Consider a random variable X with characteristic function (t) If L v(t) dt , then X has an absolutely continuous...

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Suppose that (X) is a continuous random variable that takes on real values and has characteristic function

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Suppose that $X$ is a continuous random variable that takes on real values and has characteristic function $\psi(t)=\exp (-|t|)$. Use Theorem 2.28 to find the density of $X$.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:00 AM

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Suppose that (X) is a continuous random variable that takes on real values and has characteristic function

Question:

Theorem 2.28. Consider a random variable X with characteristic function (t). If L** \v(t)]dt < , then X has an absolutely continuous distribution F with a bounded and con- tinuous density f given by 1 f(x) = 2 exp(-itx)(t)dt.

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Introduction To Statistical Limit Theory

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