I'm working on a problem where I'm given the cumulative probability density function (F(x)=1-x-5, x>1). To get the expected value, I integrated 1-F(x) over 1 to infinity. When I do this, I get 0.25.
When I take the derivative to get the pdf, I get f(x)=5x-4. When I integrate xf(x) from 1 to infinity, I get 1.25.
Why am I getting different values? The answer is definitely 1.25. I thought that to get the expected value, you could integrate either xf(x) or 1-F(x) over the range of possible values. Is this not universally true? Or am I missing something?
Any help would be greatly appreciated. Thanks in advance.
Peter
When I take the derivative to get the pdf, I get f(x)=5x-4. When I integrate xf(x) from 1 to infinity, I get 1.25.
Why am I getting different values? The answer is definitely 1.25. I thought that to get the expected value, you could integrate either xf(x) or 1-F(x) over the range of possible values. Is this not universally true? Or am I missing something?
Any help would be greatly appreciated. Thanks in advance.
Peter