Normal Distributions, need urgent help!

[thelazyman]

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!

 

[Deleted member 4993]

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!

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.

 

[thelazyman]

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.