For a random variable X with PMF show that EaX b aEX b wh

For a random variable X with PMF show that E[aX + b ] = aE[X] +b, where a and b are scalars. For a random variable X with PMF px (:r), show that vara(ax + b) - a2 var(x), where a and b are scalars. For random variables X and Y with joint PMF y), show that E[X + 1] = E[X] + E[Y]. Note that X and Y are not necessarily independent. Given the properties in parts (a) and (c), express E[aX + bY + c] in terms of E[X] and E[Y].

Solution