If N(4,2) means a distribution with a mean of 4 and standard deviation of 2, etc. and 2X +Y is a distribution made up of twice as many from group X as group Y,
then the mean of the combined group is
(2*4 + 10)/3 = 6,
and the new standard deviation is
sqrt[(2^2 + 2^2 + 1^2)/3] = sqrt3 = 1.73
Suppose X is N(4,2) and Y is N(10,1). what kind of distribution is 2X+Y? What is its mean and standard deviation if X and Y are independent?
2 answers
My answer was a guess. It is probably wrong regarding the standard deviation. A non-normal "bipolar distribution" is possible when two different populations are mixed.