What is the covariance between x and y


Let a random variable X be distributed as N(0,1). Now suppose that a second random variable, Y, is constructed as the product of X and an independent random variable Z, which equals 1 with probability ½ and -1 with probability ½. What is the (marginal) distribution of Y? What is the covariance between X and Y? What is the distribution of X conditional on Y?

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Microeconomics: What is the covariance between x and y
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