Question: 2. [6 points] Let X and Y be normal random variables with means 0 and 1 , respectively, and variances I and 4 , respectively.

2. [6 points] Let X and Y be normal random variables with means 0 and 1 , respectively, and variances I and 4 , respectively. a) [2 Points] Find P(X1.5) and P(X1) b) [2 Points] Find the probability density function (PDF) of (Y1)/2. c) [2 Points ] Find P(1Y1). Hint: Use the even symmetry property of Gaussian PDF

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