# Thread: How can I solve this expected value equation?

1. ## How can I solve this expected value equation?

The equation is E[f(X)] x E[X] = 1 where X is a continuous random variable with its expected value and distribution unknown and f is a function that transforms X. I need to solve for a formula for f. How can I do this? Is it even possible without additional assumptions?

2. ## Re: How can I solve this expected value equation?

Are there restrictions on the properties that f must have? Does f need to be the same regardless of what we choose for the excited value of X?

3. ## Re: How can I solve this expected value equation?

The only property f needs is the equation above. It can even be constant. I have to compute 1/E[X] by sampling f(X) rather than computing E[X] and taking its inverse because of the framework I am using.

4. ## Re: How can I solve this expected value equation?

So using f(x) = 1/E[X] wouldn't work for you then huh?

5. ## Re: How can I solve this expected value equation?

Unfortunately, I can't compute E[X] as I only have a single sample of X to work with.

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