What's the meaning of this expression?

[brorsonyao]

Homework Statement

E(Vq | p) ≥ p

p = price q = quality V = value

The Attempt at a Solution

Well, it's something to do with expected value to be greater or equal to price, but that's as far as I get really. Don't get what this means (Vq | p). Any help is appreciated!

 

[Office_Shredder]

It seems to be saying that:

The expected value of Vq (V times q) given p

To account for conditional expectation you simply need to make all your probabilities conditional in the formula you have for expectation

 

[HallsofIvy]

Well, since "V= value" and "q= quality", then "Vq" is "value times quality". The "|" in a probability problem typically means "given that". The is saying that, given a specific price, the "value times quality" will be greater than or equal to that price. I'm not sure what you mean by "value" or "quality" (did you mean "quantity") are but presumably they depend on the price.

 

[brorsonyao]

Hi,

Actually, although it says Vq, I think it means V(q). This would mean: given the price, p, the expected value of the object, which depends on its quality, is greater or equal to p? Sounds a bit strange, though, I think?

 

[HallsofIvy]

The meanings of variables is not a "mathematics" question so I am no expert but I would suspect this is talking about the estimated value of some object you are considering buying. Obviously the value to you is a function of its perceived "quality". Just as obviously, you will only buy it if you estimate its value to be greater than the price you would have to pay.