If two random variables X and Y are independent and have Nor

If two random variables X and Y are independent and have Normal distributions with means and variances _X, _Y, ²_X, ²_Y respectively then the distribution of aX + bY is also normal with mean a_X + b_Y, and variance a²²_X + b²²_Y. Given that: _X=30, _Y= 10, ²_X= 4, ²_Y=9.

a.) Find the mean and standard deviation of 2X + 3Y

b.) Find the mean and standard deviation of 2X - 3Y

c.) Calculate P(15 < X - Y < 25)

Solution