Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)). Let Y be a random variable distributed as a Normal with mean 2 and variance 3 (i.e.., Y ~ N(2, 3)). X and Y are independent. What is the distribution of 2X – 5Y ?

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Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)). Let Y be a random variable distributed as a Normal with mean 2 and variance 3 (i.e.., Y ~ N(2, 3)). X and Y are independent. What is the distribution of 2X – 5Y ?

O a. 2X- 5Y ~ N(10,-67)
O b. 2X - 5Y -
O c. 2X - 5Y - N(-10, 19)
N(10, -67)
N(-10,83)
d. 2X – 5Y ~ N(10, 83)
Transcribed Image Text:O a. 2X- 5Y ~ N(10,-67) O b. 2X - 5Y - O c. 2X - 5Y - N(-10, 19) N(10, -67) N(-10,83) d. 2X – 5Y ~ N(10, 83)
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