# Thread: Trying to prove E(X) and E(2X) for beta distribution

1. ## Trying to prove E(X) and E(2X) for beta distribution

Im trying to formulate a couple of proofs that shows how E(x)=a/a+b and E(2x)=(a(a+1))/((a+b)(a+b+1) are derived for the beta distribution. I have no problem with the MGF of other functions, but this one is so complicated. I really dont know where to start, sorry

2. Originally Posted by nine4fours
Im trying to formulate a couple of proofs that shows how E(x)=a/a+b and E(2x)=(a(a+1))/((a+b)(a+b+1) are derived for the beta distribution. I have no problem with the MGF of other functions, but this one is so complicated. I really dont know where to start, sorry

Now apply the definition of E(X) and do the calculation. Note that E(2X) = 2 E(X).

3. Originally Posted by mr fantastic

Now apply the definition of E(X) and do the calculation. Note that E(2X) = 2 E(X).
I assume he/she meant the second moment, $\displaystyle E(X^2)$.

4. Originally Posted by matheagle
I assume he/she meant the second moment, $\displaystyle E(X^2)$.
Darn it. I was waiting for the OP to correct me .....

5. Originally Posted by mr fantastic
Darn it. I was waiting for the OP to correct me .....

you can delete my message then.
I assume op=original (im)poster?
and not ron howard (Opie)

6. Originally Posted by matheagle
you can delete my message then.
I assume op=original (im)poster?
and not ron howard (Opie)
Correct.

(And don't think I haven't noticed how hard you're trying to snatch both my hard earned Awards. Game on with Funniest Member, matheagle ..... Stay tuned ).

7. My favourite, which I'm sure you'll steal, lol,
is when these probability books use U as a rv.
Then I have to say FU to my class repeatedly, as in $\displaystyle f(u)$.