Question

A drunkard executes a “random walk” in the following way: each minute he takes a step north or southm with probability 1/2 each, and his successive step directions are independent. His step lenght is 50 cm. Us the central limit theorem to approximate the probability distribution of his location after 1h. Where is he most likely to be?

Answer 1

You should get the mean through:

Mean= 50 (1/2)- 50(1/2) which will give you zero.

Second, you will get the standard deviation.

Then multiply it 50 by 60

So:

50 (60) = 300

Square root of 300 = 17.32.

Through this, you can say that he is just near to the place where he is walking after 1 hour.