Hi In the notes, section 4.2, there is a question which determines the distribution of 2X-Y (X and Y independent standard normal dist). Within the calculation it shows calculation of variance by multiplying 1 by the square of coefficients of 2X+Y i.e. 2X-Y ~ N(2*0 - 0, 2^2 *1 + (-1)^2 *1) to get N(0,5) However, in question 4.7 of practice questions, when calculating the combined distribution it multiplies the individual variances by just the coefficient, without squaring i.e. ~ N(3*2100 - 4*800, 3 *300^2 + 4 *100^2) Is there a reason why they are different? is it because each individual claim size is normally distributed, therefore there are 3 or 4 instances of the random variables (i.e. Yi and Xi), as opposed to the same 2 random variable applied 3 or 4 times (i.e. not 3Y - 4X)?
