expected value and variance help

danicathea

New member
Joined
Jul 23, 2013
Messages
4
Hi,

I need to find a probability density function f(x) such that a random variable X with f(x) as its probability density function does have a well defined expected value E(X), but does not have a well defined variance Var(X). So basically E(X) exists but Var(X) does not. The function has to met the requirements that it needs to have f(x)> or equal 0 be integrable and it bust f(x)dx=1 from negative infinity to positive infinity.

I am very confused by this not sure if I just try different functions which would take me forever to do I think.

Thank you
Amy G
 
Last edited:
Hi,

I need to find a probability density function f(x) such that a random variable X with f(x) as its probability density function does have a well defined expected value E(X), but does not have a well defined variance Var(X). So basically E(X) exists but Var(X) does not. The function has to met the requirements that it needs to have f(x)> or equal 0 be integrable and it bust f(x)dx=1 from negative infinity to positive infinity.

I am very confused by this not sure if I just try different functions which would take me forever to do I think.

Thank you
Amy G

What does that mean?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

[url]http://www.freemathhelp.com/forum/th...217#post322217[/URL]

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")
 
Hi,

I need to find a probability density function f(x) such that a random variable X with f(x) as its probability density function does have a well defined expected value E(X), but does not have a well defined variance Var(X). So basically E(X) exists but Var(X) does not. The function has to met the requirements that it needs to have f(x)> or equal 0 be integrable and it bust f(x)dx=1 from negative infinity to positive infinity.

I am very confused by this not sure if I just try different functions which would take me forever to do I think.

Thank you
Amy G
HINT: if the tails of the distribution asymptotically decay as f(x)~1/x^2, then the integral of x^2*f(x) will not converge. 2nd HINT: At x=0, you need the function to be a constant (that is, it can't just be 1/x^2).

I had another answer ready to post, but I don't want to spoil all your fun. If these hints aren't sufficient, repost and show us what you have tried.
 
So do I try to integrate a funciton such as 1-(1/x^2) from negative infinity to infintity cause I don't really understand integrating cuz when i did it my self I took out the 1 and was left with -(1/x^2). In which I was going to use parts to solve the x^2 to make sure its value does not go to infinity.
 
So I ended up getting a value of 1 when doing the E(X)=f(x)dx I feel as though I went very wrong somewhere and when I do the varience I get a numerical value is that whats supposed to happen.
 
Top