What is the expected value of a particle's position after n jumps?

[uva123]

Homework Statement

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 particle 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.

Homework Equations

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

The Attempt at a Solution

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

 

[rock.freak667]

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

 

[uva123]

im really not sure.

 

[rock.freak667]

im really not sure.

Which distributions do you know?