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Distributionshard
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Let X∼N(0,1)X \sim N(0, 1)X∼N(0,1) and let Φ(x)\Phi(x)Φ(x) be the cumulative distribution function of the standard normal distribution. Evaluate the expectation E[Φ(X)2]E[\Phi(X)^2]E[Φ(X)2].