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Q7Section I (Objective (Q1–Q80))7 of 80

Distribution Theory — double integral of independent normal densities over a disk

If φ(.)\varphi(.) is pdf of N(0,1)N(0, 1) distribution and A represents a circle of unit area with centre at origin, then what is the value of ∬Aφ(x)φ(y) dx dy\iint_{A} \varphi(x)\varphi(y)\, dx\, dy?

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