Let X and X be IID Gaussian random variables with Xi~ N(0,02), i = 1,2. Let...

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Let X₁ and X₂ be IID Gaussian random variables with Xi~ N(0,02), i = 1,2. Let Y = X₁ + X₂. Then answer the following questions. (a) Find the distribution of Y by using functions of random variable' approach. You can use the convolution of pdf formula if it is required. (b) Find the conditional distribution of X₁ given Y = y. Interpret the result obtained. What will you expect the conditional distribution of X2 given Y = y to be? Let X₁ and X₂ be IID Gaussian random variables with Xi~ N(0,02), i = 1,2. Let Y = X₁ + X₂. Then answer the following questions. (a) Find the distribution of Y by using functions of random variable' approach. You can use the convolution of pdf formula if it is required. (b) Find the conditional distribution of X₁ given Y = y. Interpret the result obtained. What will you expect the conditional distribution of X2 given Y = y to be?

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