Question

X and Y are independent random variables with E(X)=8,σ2X=4, E(Y)=4 and σ2Y=6. Then E(12X+6Y)=?

Answer 1

Answer:

If X and Y are continuous variables, then P(X+Y=3)=0.P(X+Y=3)=0. If X and Y are discrete, then the probability is not 0 but there is no way to know what it is from the information given.

In fact, for any number of continuous variables (1 or 2 or more) and for any value, the probability that the sum will be that value is 0.

If, instead, you mean P(X+Y>0)P(X+Y>0) then there is no way to know from the information given.

In fact, it's hard to think of any question about the probability that can be answered from the information given.