Standard deviation of random walk

1. What is the variance of a random walk?
2. Is the variance of a random walk constant?
3. What is distribution of random walk?
4. What is random walk formula?

What is the variance of a random walk?

The variance of a random variable X is defined as var[X] = E[(X −E[X])2]. In other words, on average, what is the square of your distance to the expectation.

Is the variance of a random walk constant?

It can be shown that the mean of a random walk process is constant but its variance is not. Therefore a random walk process is nonstationary, and its variance increases with t.

What is distribution of random walk?

Random walk theory suggests that changes in stock prices have the same distribution and are independent of each other. Therefore, it assumes the past movement or trend of a stock price or market cannot be used to predict its future movement.

What is random walk formula?

yn=12(1+xn). Since yn takes the values 0 and 1 with equal probability, xn takes the values –1 and +1 with equal probability—so xn is identical to our random walk one-step variable above.