- #1

- 13

- 0

-(1-F(x/a))f(1/a)

or

-(1-F(x/a))f(x/a).

Also, I am not sure how to interpret the result that at the maximum:

F(x/a)f(x/a)=1.

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- Thread starter ruzbayhhi
- Start date

- #1

- 13

- 0

-(1-F(x/a))f(1/a)

or

-(1-F(x/a))f(x/a).

Also, I am not sure how to interpret the result that at the maximum:

F(x/a)f(x/a)=1.

- #2

- 649

- 2

I am trying to take a derivative of (1-F(x/a))(x) (where F(.) is a CDF and a is a parameter).

This expression seems a bit strange. The part within the first parenthesis, 1-F(x/a), is just a real number, but you seem to be evaluating it at x?

- #3

- 13

- 0

- #4

- 649

- 2

From this description, I calculated A, the average "income" or "payoff" for the seller, to be the same result as you:

A = x*(1-F(x/a))

I don't want to risk doing other peoples assignments and so on, but I will say that the chain rule of differentiation applied to F(x/a) would be

d/dx F(x/a) = f(x/a) * 1/a

where f is the probability density corresponding to the CDF F. Reason: you differentiate F(x/a) with respect to ITS argument x/a, and get f(x/a). Then you multiply this by the derivative of THAT argument x/a with respect to x, which is 1/a.

- #5

HallsofIvy

Science Advisor

Homework Helper

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- 969

What is "f"? The derivative of F?

If so then the derivative of (1- F(x/a))x is

(1- F(x/a))- f(x/a)(x/a)

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