Calculating Expected Value of a Random Variable: Solving for E[X]

[changeofplans]

Homework Statement

Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X]

Homework Equations

The Attempt at a Solution

I'm not sure how to start this. A push in the right direction would be awesome.

Thanks!

 

[LCKurtz]

Homework Statement

Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X]

Homework Equations

The Attempt at a Solution

I'm not sure how to start this. A push in the right direction would be awesome.

Thanks!

I will call $P(X=i) = p_i$ to save typing. You can get $p_2$ and $p_3$ in terms of $c$ and $p_0$. You know the $p_i$ add to 1. That will give you an equation with $c$ and $p_0$. Crank out the formula for $E(X)$ and you should be able to get an answer that depends on $c$.