# 3.13.4 Example Continued: Simplified Representation of a Quadratic Polynomial of a Multivariate Normal Random Vector

###### 3.13.4  Example (Continued)

Continuing with our earluer example, consider again the random variable Y defined by [3.168] as a quadratic polynomial of a joint-normal random vector X. Let’s calculate its first five moments. Earlier, we were given values for μ, c, b and a. We calculated values for and . Based on all these values, we use [3.181] to calculate values for g[k] as indicated in Exhibits 3.25. Moments of Y are calculated from these by [3.183] through [3.187]. Results are indicated in Exhibit 3.26.

Exhibit 3.25: Using formula [3.181], g[k] values are calculated for the random variable Y defined by [3.168].
Exhibit 3.26: Moments are indicated for the random variable Y defined by [3.168]. Computations are performed according to [3.183] through [3.187]. Inputs are the values of Exhibit 3.25.