(Linear combinations). For the purpose of this question, the random variables X and Y are independent...

(Linear combinations). For the purpose of this question, the random variables X and Y are independent normal X ∼ N(12, 3) and Y ∼ N(15, 4), where the two arguments are the mean and standard deviation, so the variances are 9 and 16 respectively. If a, b are two constants, the linear combination aX +bY is normally distributed with mean 12a + 15b and variance 9a 2 + 16b 2 . Hence or otherwise, compute the following probabilities:

Part a: P(Y < 17) =

Part b: P(X ≥ 10) =

Part c: P(X + Y < 20) =

Part d: P(|Y − X| < 1) =

Part e: P(Y < X) =

Part f: P(Y = 15) =

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orchestra answered 2 years ago

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(Linear combinations). For the purpose of this question, the random variables X and Y are independent...

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