14. Correct. The answer is true
The expected value of copper given that 2,000 tons of molybdenum has been discovered is described by the equation:
E[Y|X=2000] =
500(.10/.15)+750(.05/.15) = 583.33 tons.
Also, the expected values of copper given that 1,000
and 500 tons of molybdenum have been discovered are described by the respective
equations:
E[Y|X=1000]
= 500(.10/.35)+750(.25/.35) = 678.57 tons and
E[Y|X=500]
= 500(.25/.50)+750(.25/.50) = 625 tons.
The conditional variance of molybdenum given that 750 tons of copper has been discovered is described by the following equation:
Var
[X|Y=750] = ∑
(X- E[X|Y=750])2*P[X=Xi
| Y=750]
Var [X|Y=750] = (2000-863.64)2 (.05/.55) + (1000-863.64)2 (.25/.55) + (500-863.64)2 (.25/.55) = 185,950.41,
Where
E[X|Y=750] = 2000(0.5/.55)+1000(.25/.55)+500(.25/.55) =
863.64
The conditional standard deviation of:
Var [X|Y=500] = (185,950.41)0.5 = 431.22.