IGNORE "MODULE 10", the information here should be enough to solve the question. USE MATLAB to solve.

We will write a function wiener.m to construct a sample path of a Wiener random pro- cess 0n the interval [0,1] as the limit of a discretetime random walk following the steps outlined in the Module 10 screencasts. The function call will be the following: [X,t] = Wiener (T,alpha);,where alpha will be the ratio of the step size squared to time interval sg/T, T will be the time step, Z will be the vector process values at the times in the vector t. Again, each step below will form a line of the program: 9 (i) First generate the set of time points we will use based on the input information: t = 0:T:1; 0 (ii) Next, set the step size s of the discrete random walk. For convergence, we required that this step size scale with the time interval as s2 / T = a s = sqrt (alpha*T); 0 (iii) Generate a random vector of positive and negative jumps of size s by scaling Bernoulli trials (which we generate by rounding uniform random variables to :|:1):. z round(rand(length(t) , 1)) ; jumps s*( sign(z - .5) ); 0 (iv) Finally, we generate the Wiener process value at each time as the cumulative sum of the jumps: X = cumsum(jumps); 7 POINTS Add these steps together to create your program and generate a few sample paths of the Wiener process for various choices of the parameter alpha. You can plot your sample paths via plot (1: ,X)