Let Y₁, Y2, Y3 be i.i.d. N(0, 1) random variables. (a) Give values of a and b such that: (b) Show that: a(Y₁ - Y₂)² + b(Y₁ + Y₂)² ~ x² 1 [(Y1 − Y2)² + (Y2 − Y3)² + (Y3 − Y1)²] ~ x² انت

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Let Y₁, Y2, Y3 be i.i.d. N(0, 1) random variables.
(a)
Give values of a and b such that:
Show that:
a(Y₁ - Y₂)² + b(Y₁ + Y₂)² ~ x²
1
½ [(Y₁ − Y₂)² + (Y2 − Y3)² + (Y3 − Y₁)²] ~ x²
Transcribed Image Text:Let Y₁, Y2, Y3 be i.i.d. N(0, 1) random variables. (a) Give values of a and b such that: Show that: a(Y₁ - Y₂)² + b(Y₁ + Y₂)² ~ x² 1 ½ [(Y₁ − Y₂)² + (Y2 − Y3)² + (Y3 − Y₁)²] ~ x²
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