Exam MAS-I Practice Question 171
Study guide: Exam MAS-I
X_1, \dots, X_5 are independent normal variables with common variance \sigma^2 and means \mu_1, \dots, \mu_5, not all zero. The statistic Y = \sum_{i=1}^{5} X_i^2/\sigma^2 has a noncentral chi-squared distribution with 5 degrees of freedom and noncentrality parameter \theta = \sum_{i=1}^{5} \mu_i^2/\sigma^2 = 3.
Determine E[Y] and \text{Var}(Y).
- A)
E[Y] = 5and\text{Var}(Y) = 10 - B)
E[Y] = 8and\text{Var}(Y) = 16 - C)
E[Y] = 8and\text{Var}(Y) = 22 - D)
E[Y] = 11and\text{Var}(Y) = 22 - E)
E[Y] = 11and\text{Var}(Y) = 34
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