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If X and Y are normally distributed and are uncorrelated, then they might still be dependent! Suppose that X is a standard normal distribution. Let

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If X and Y are normally distributed and are uncorrelated, then they might still be dependent! Suppose that X is a standard normal distribution. Let s be a random variable, independent of X, which takes values in {1, 1), each with probability 1/2. ~ (a) Find the distribution of Y = EX.

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