Biased coin toss and random walk Consider the following random walk model. Let the starting position Xo = 0 be deterministic. At each time t you flip a fair coin and add 1 to X-1 if you see heads H, else add -1 if you see tails T. Suppose the first 9 coin flips result in the sequence HTTTHHTTT. Suppose now that the coin you flip is biased with P(H) = 3/4 and P(T) = 1/4 %3D %3D Find the expected position E [X10] at time t = 10. Find the expected position E [X20] at time t = 20. Find the variance of the position X10 at time t = 10. Find the variance of the position X20 at time t = 20. What is the slope of the drift of this random walk? Find the forecast E[X10|X9]. 0.5 O X9 O (X1+...+X9) /9 O X, + 0.5 O (X1+...+Xg)/9+0.5