### Random Walk and 1-Dimensional Heat Equation and its Fundamental Solution

Suppose that a particle, starting at the origin, has an equal chance of moving to the left or right by a distance ∆x in a time interval of ∆t. (a) Let n>0 be an integer, and let m be an integer, such that -n≤m≤n and n-m is even. By computing the number of ways that the particle can move a net distance