a. Prove that (kappa_{4}=mu_{4}^{prime}-4 mu_{3}^{prime} mu_{1}^{prime}-3left(mu_{2}^{prime}ight)^{2}+12 mu_{2}^{prime}left(mu_{1}^{prime}ight)^{2}-6left(mu_{1}^{prime}ight)^{4}). b. Prove that (kappa_{4}=mu_{4}-3 mu_{2}^{2}), which is often called the

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a. Prove that $\kappa_{4}=\mu_{4}^{\prime}-4 \mu_{3}^{\prime} \mu_{1}^{\prime}-3\left(\mu_{2}^{\prime}ight)^{2}+12 \mu_{2}^{\prime}\left(\mu_{1}^{\prime}ight)^{2}-6\left(\mu_{1}^{\prime}ight)^{4}$.

b. Prove that $\kappa_{4}=\mu_{4}-3 \mu_{2}^{2}$, which is often called the kurtosis of a random variable.

c. Suppose that $X$ is an $\operatorname{Exponential}(\theta)$ random variable. Compute the fourth cumulant of $X$.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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a. Prove that (kappa_{4}=mu_{4}^{prime}-4 mu_{3}^{prime} mu_{1}^{prime}-3left(mu_{2}^{prime}ight)^{2}+12 mu_{2}^{prime}left(mu_{1}^{prime}ight)^{2}-6left(mu_{1}^{prime}ight)^{4}). b. Prove that (kappa_{4}=mu_{4}-3 mu_{2}^{2}), which is often called the

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Introduction To Statistical Limit Theory

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