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A drunken man walks on a straight lane. At every integer time (in seconds) he moves a distance of $1$ unit randomly, either forwards or backwards. What is the expectation of the square of the distance after $100$ seconds from the initial position? Hint: The position at time $100$ is a sum of independent and identically distributed random variables.

  1. $100$
  2. $\frac{\sqrt{300}}{4}$
  3. $40$
  4. $200$
  5. $20 \pi$

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