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6. Suppose Xxi and V(X) = 8. Find E(X³)

6. Suppose Xxi and V(X) = 8. Find E(X³)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question 6:** Suppose \( X \sim \chi^2_k \) and \( V(X) = 8 \). Find \( E(X^3) \). --- **Explanation:** This is a statistical problem involving a chi-squared distribution with \( k \) degrees of freedom. Given \( V(X) \), which denotes the variance of \( X \), is 8, the task is to find the expected value of \( X^3 \), denoted as \( E(X^3) \). In chi-squared distributions, the variance and moments are related to the degrees of freedom, \( k \). The variance \( V(X) \) is equal to \( 2k \), so you can use this to determine the value of \( k \). Once you have \( k \), you can find \( E(X^3) \) using properties of the chi-squared distribution.
Transcribed Image Text:**Question 6:** Suppose \( X \sim \chi^2_k \) and \( V(X) = 8 \). Find \( E(X^3) \). --- **Explanation:** This is a statistical problem involving a chi-squared distribution with \( k \) degrees of freedom. Given \( V(X) \), which denotes the variance of \( X \), is 8, the task is to find the expected value of \( X^3 \), denoted as \( E(X^3) \). In chi-squared distributions, the variance and moments are related to the degrees of freedom, \( k \). The variance \( V(X) \) is equal to \( 2k \), so you can use this to determine the value of \( k \). Once you have \( k \), you can find \( E(X^3) \) using properties of the chi-squared distribution.
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