Suppose that {X1, X2, X3} are statistically independent Gaussian random variables with P₁ = E{X₁} = 0 and var (X₁) = o2 for i = 1, 2, 3. a) Are (X1, X2, X3} jointly Gaussian? Please explain. Find the joint pdf of the three random variables. b) Let Y₁ (2) -(17¹) (X₂) explain. = c) Find cov(Y2, X2). Are {Y₁, Y2} statistically independent? Please

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Suppose that {X1, X2, X3} are statistically independent Gaussian random variables with
P₁ = E{X₂} = 0 and var (X₁) = o2 for i = 1, 2, 3.
a) Are {X₁, X2, X3} jointly Gaussian? Please explain. Find the joint pdf of the three
random variables.
b) Let
* (X) = (17) (X). Are {Y₁, Y2} statistically independent? Please
Y₂
explain.
c) Find cov(Y2, X2).
Transcribed Image Text:Suppose that {X1, X2, X3} are statistically independent Gaussian random variables with P₁ = E{X₂} = 0 and var (X₁) = o2 for i = 1, 2, 3. a) Are {X₁, X2, X3} jointly Gaussian? Please explain. Find the joint pdf of the three random variables. b) Let * (X) = (17) (X). Are {Y₁, Y2} statistically independent? Please Y₂ explain. c) Find cov(Y2, X2).
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