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Let U be a chi-square random variable with one degree of freedom. Let W be a random variable independent of U, which is +-1 with

Let U be a chi-square random variable with one degree of freedom. Let W be a random variable independent of U, which is +-1 with probability of 1/2 each. Using only U and W, construct a normal random variable. You need to show that the random variable has the standard normal distribution

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