Simulate a time series of T error terms t(i), t = 1, . . . , T distributed as N(0, 1). T is the length

1. Simulate a time series of T error terms εt(i), t = 1, . . . , T distributed as N(0, 1). T is the length of your  series.

2. Compute a time series of prices, assuming that they are driven by a random walk pt(i) = pt-1(i) + εt(i).

3. Estimate the AR(1) model pt(i) = α(i) + β(i)pt-1(i) + ut(i).

4. Compute the test statistic t(β(i)) for the null hypothesis from the DF test.

I have to do this on python but I don't know how.