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Distributionshard
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For a standard normal random variable Z∼N(0,1)Z \sim N(0, 1)Z∼N(0,1), which of the following functions g(x)g(x)g(x) satisfies the inequality P(Z>x)>g(x)ϕ(x)P(Z > x) > g(x) \phi(x)P(Z>x)>g(x)ϕ(x) for all x>0x > 0x>0, where ϕ(x)\phi(x)ϕ(x) is the probability density function of ZZZ?