I understood that if X and Y are random variables, we can let Z be a linear combination of them
Z = aX + bY
where a and b are given constants.
then the expected value would be
E[Z] = aE[X] + bE[Y]
However, I'm unsure about how the constants should be used. If X is the result of rolling a 6-sided fair dice and Y is the result of an 8-sided dice, what would it mean to let a = 2 and b = - 3 for example?
Would it mean that we double the result of the 6-sided dice and multiply the result of the 8-sided dice by -3 and let Z be the combined result?
Z = aX + bY
where a and b are given constants.
then the expected value would be
E[Z] = aE[X] + bE[Y]
However, I'm unsure about how the constants should be used. If X is the result of rolling a 6-sided fair dice and Y is the result of an 8-sided dice, what would it mean to let a = 2 and b = - 3 for example?
Would it mean that we double the result of the 6-sided dice and multiply the result of the 8-sided dice by -3 and let Z be the combined result?