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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

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 1/2 each. Using only U and W , construct a standard normal random variable. You need to show that this random variable has the standard normal distribution to receive full credit.

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