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Let X, Y be independent N(0, 1), N(1, 2) random variables, respectively, where the notation N(, 2 ) refers to a normal random variable with

Let X, Y be independent N(0, 1), N(1, 2) random variables, respectively, where the notation N(, 2 ) refers to a normal random variable with mean and variance ^2 . Find P[2X > Y ].

Hint. What is the distribution of a linear combination of independent normals?

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