**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=X_{i}
| 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.