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Archer 1’s arrows land such that their distances from a perfect bull’s eye have the Normal(1,...

Archer 1’s arrows land such that their distances from a perfect bull’s eye have the Normal(1, 1) distribution, while the distances of Archer 2’s arrows from a perfect bull’s eye have the Normal(0, 2) distribution. Assuming their shots are independent, find the probability that on a given shot, Archer 1 hits closer to a bull’s eye than Archer 2.

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Answer #1

According to the question,Archer 1’s arrows land such that their distances from a perfect bull’s eye have the Normal(1, 1) distribution, while the distances of Archer 2’s arrows from a perfect bull’s eye have the Normal(0, 2) distribution.

Also, we assume that their shots are independent.

Define, archer 1's arrow shot distance from the perfect bull's eye= X &

archer 2's arrow shot distance from the perfect bull's eye= Y

Then,

P(Archer 1 hits closer to a bull’s eye than Archer 2)

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