If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = ________.
Correct Answer
Solution & Step-by-step Explanation
In the range: 11 - 11
Concept:
E[x + y] = E[x] + E[y]
E [Ax] = A E[x]
Where E [x] represents the expected or mean value of the random variable 'x'
Application:
E[2x + y] = 0
2E[x] + E[y] = 0 ----(1)
E[x + 2y] = 33
E[x] + 2E[y] = 33 ----(2)
Adding (1) and (2)
3E[x] + 3E[y] = 33
E[X] + E[Y] = 11
Concept:
E[x + y] = E[x] + E[y]
E [Ax] = A E[x]
Where E [x] represents the expected or mean value of the random variable 'x'
Application:
E[2x + y] = 0
2E[x] + E[y] = 0 ----(1)
E[x + 2y] = 33
E[x] + 2E[y] = 33 ----(2)
Adding (1) and (2)
3E[x] + 3E[y] = 33
E[X] + E[Y] = 11