Question: 2. (10 points) Suppose random variable U Uniform(0, 1). Let Y = ln(1 U) where is a positive constant. (a) Derive the distribution of the

2. (10 points) Suppose random variable U Uniform(0, 1). Let Y = ln(1 U) where is a positive constant. (a) Derive the distribution of the random variable Y . Write the down the pdf of Y including its support and also identify the distribution of Y by name specifying its parameter value/values. [Hint: either the distribution function method or method of univariate Jacobian transformation can be used here.] (b) Does 2Y/ follow a chi-square distribution? Justify your answer whether you agree or disagree. If yes, what are its degrees of freedom. [Hint: use any method you like.]2. (10 points) Suppose random variable U Uniform(0, 1). Let Y = ln(1 U) where is a positive constant. (a) Derive the distribution of the random variable Y . Write the down the pdf of Y including its support and also identify the distribution of Y by name specifying its parameter value/values. [Hint: either the distribution function method or method of univariate Jacobian transformation can be used here.] (b) Does 2Y/ follow a chi-square distribution? Justify your answer whether you agree or disagree. If yes, what are its degrees of freedom. [Hint: use any method you

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