Normal Distributions, need urgent help!

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thelazyman

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Jan 14, 2006
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58
The question asks, if X ~ N (10,3) and Y~ N (15,8), and if X and Y are independent, what is the probability distribution of 4X + 5Y?

I dont know where to start with this, inputting the values for x, and only got 52, the answer they got is: 4X + 5Y ~ N(115,248), but dont know how they got it, any help or explanation would be appreciated, thanks!
 
thelazyman said:
The question asks, if X ~ N (10,3) and Y~ N (15,8), and if X and Y are independent, what is the probability distribution of 4X + 5Y?

I dont know where to start with this, inputting the values for x, and only got 52, the answer they got is: 4X + 5Y ~ N(115,248), but dont know how they got it, any help or explanation would be appreciated, thanks!
Click to expand...
Hint:

115 = 4*10 + 5*15

Did you consult your textbook?

Please show us your work, indicating exactly where you are stuck, so that we may know where to begin to help you.
 
Well for that question, i tried to get the Y value, i got the X value from the sample means, but I dont know where the y values come from, like i do not know if it comes from the variance, so that is what i am trying to figure out.
 
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