Find c for Random Variable: E(X), E(X^2), E(1/X) & Var(X)

[Firepanda]

a discrete random variable has range space {1, 2, ..., n} and satisfies P(X=j) = j/c for some number c. Find c, and then find E(X), E(X^2), E(1/X) and Var(X).

thanks

 

[maverick280857]

What is your solution?

You have the probability mass function (pmf). You can determine the constant c.

The expectations are obtained directly by definition...

 

[Firepanda]

What is your solution?

You have the probability mass function (pmf). You can determine the constant c.

The expectations are obtained directly by definition...

Thanks for your reply.

Sorry I should have stated before that I don't know where to start on this.

I just looked up on pmf, and I have no examples on a question like this in my notes.

The 'j' confuses me in the question as I don't see how it relates to anything else, so finding c is tricky for me.

Thanks

 

[quadraphonics]

Sorry I should have stated before that I don't know where to start on this.

Well, aren't there a few conditions that all valid pmf's are required to satisfy? It would probably be a good idea to review these.

The 'j' confuses me in the question as I don't see how it relates to anything else, so finding c is tricky for me.

j is simply a dummy variable. Just shorthand for saying P(X=1) = 1/c, P(X=2) = 2/c, ..., P(X=n) = n/c.

Perhaps this thread should be moved to the homework help section?

 

[Firepanda]

The conditions I know of pmf are that the total sum of the probabilities from -infinity to infinity is 1, and the probabilities can only take values between 0 and 1.

So do I have to find a j/c which has a sum of the series from -infinity to infinity equal to 1?

Sorry I'm really confused..

ok so I have so far:

1/c + 2/c + 3/c ... +n/c = 1

1 + 2 + 3 +.. + n = c

c = infinity?

 

[exk]

a pmf is for a discrete random variable.

Do you know what the definition of a discrete RV is?

Otherwise you have the right idea. c doesn't have to equal infinity. what is the sum of n consecutive integers?

 

[HallsofIvy]

The conditions I know of pmf are that the total sum of the probabilities from -infinity to infinity is 1, and the probabilities can only take values between 0 and 1.

So do I have to find a j/c which has a sum of the series from -infinity to infinity equal to 1?

No, only 1 to n, the number over which your probability distribution is defined.

Sorry I'm really confused..

ok so I have so far:

1/c + 2/c + 3/c ... +n/c = 1

1 + 2 + 3 +.. + n = c

c = infinity?

Why should it be? n is a fixed finite number, not "infinity". Do you know the formula for the sum of the first n positive integers?