Random Variable Probability Distribution

[DualDog321]

Hello, here is a problem I had trouble on:

"A random variable x has probability distribution given by P(X=x) = (x²+x)/k, for x= 1, 2, 3. Given that E(X=x)=2.5

Find k. "

Plugging in x for 1, 2, and 3, I get: 2/k, 6/k, and 12k. I think what I'm supposed to do next is sum them up to equal 1 then solve for k, which results in k=20. But, I am also confused on how I should use "E(X=x)=2.5" in this. I am not sure what "E" is.
Thank you

 

[Steven G]

For sure E must stand for expectation.
Now if you already found k and that is what you were asked to find then why do you want to use E(X=x) = 2.5?

 

[Romsek]

This is pretty dumb question. You found k by insisting that the distribution sum to one.

That E[X]=2.5 is incidental.

 

[DualDog321]

This is pretty dumb question. You found k by insisting that the distribution sum to one.

That E[X]=2.5 is incidental.

Oh, so the E(X=x)=2.5 is unnecessary information, makes sense.