# Need help with expected value

1. May 10, 2010

### uva123

1. The problem statement, all variables and given/known data

Suppose that a particle starts at the origin of the real line and moves along the line in
jumps of one unit. For each jump, the probability is p that the partical will jump one unit to the left and the probability is (1-p) that the particle will jump one unit to the right.
Find the expected value of the position of the particle after n jumps.

2. Relevant equations

E(x)=$$\sumf(x)xdx$$ from -infinity to +infinity (continuous case)
E(x)=$$\sumf(x)x$$ for all x (discrete case)

3. The attempt at a solution

p(0<p<1) =>jumps one unit left
q=(1-p) =>jumps one unit right

2. May 10, 2010

### rock.freak667

Well seeing how there are only two outcomes with n trials, how are the positions of the particle distributed?

3. May 10, 2010

### uva123

im really not sure.

4. May 10, 2010

### rock.freak667

Which distributions do you know?