Sum of squared standard normals

MediumRandom Variables Statistics~5m

$Z_1,\dots,Z_5$ are independent standard normals. What is the variance of $\sum_{i=1}^{5} Z_i^2$ ?

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Var of a sum of independents = sum of variances; find Var(Z²) first.
Var(Z²) = E[Z⁴] − (E[Z²])² = 3 − 1 = 2.

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