Marketing manager gave different proposal for allocation of money to tv advertising and other marketing methods.

He the estimated the probability for different outcomes of the proposal budget as follows

Allocation of advertising budget

Budget level old (90% tv and 10% others) New (60% Tv and 40% old)

High ---------------------------0.3 ---------- ----- -0.2---------------------

Median ------------------------0.2----------… ----------0.1-----------

Low ------- ------------------- 0.1 -------- ------------ 0.1--------------

The above is basically a table, eg the probability that high budget is used and the old allocation advertising budget is used is 0.3. To clarify further the low budget used and old allocation advertising budget used is 0.1. High budget advertising budget and high budget level is 0.2. sorry for the bad table.

The problem: for high median and low budget levels they are corresponding to 3, 2.5 and 2 million dollars respective.

a) Let the random variable X denote the proportion of budget on Tv advertising. How do I find the expected value E(X) and variance of X.

The answer for variance is 0.0216