B1&B2 HANDWRITTEN THEN BOX THE FINAL ANSWERS (DO NOT USE AI)

THE PROBLEM IS AS IS, NO OTHER REFERENCES NEEDED

I. DIFFUSION EQUATION [20 pts] Obtain the diffusion equation from the continuum limit of a random walk. II. MEAN SQUARE DISPLACEMENT IN A RANDOM WALK [20 pts] Prove that the variance in displacement of a one- dimensional random walk is proportional t0 the number Of steps. If the steps occur at regular intervals, the root mean square displacement grows as the square root of time as in diffusion