Use the result of Exercise 7 45 to show that, if n independent random variables Xi have normal distributions with the means i and the standard deviations i, then Y 1X1 2X2 anXn has a normal distribution What are the mean and the variance of this distribution ...

Use the result of Exercise 7.45 to show that, if n independent random variables Xi have normal

Question:

Use the result of Exercise 7.45 to show that, if n independent random variables Xi have normal distributions with the means µi and the standard deviations σi, then Y = α1X1 + α2X2 + · · · + anXn has a normal distribution. What are the mean and the variance of this distribution?