A laser beam has 5 gates on its route to reach a receptor. If one gate is closed, the light cannot continue its path and therefore, cannot reach the receptor. The probability that a given gate is open is 1/3.

• (a) Write the pmf of the random variable X = "number of gates passed by the laser beam before the first stop occurs".
• (b) Compute its expected value and variance.
  

5. A laser beam has 5 gates on its route to reach a receptor. If one gate is closed, the light cannot continue its path and therefore, cannot reach the receptor. The probability that a given gate is open is 1/3. (a) Write the pmf of the random variable X = "number of gates passed by the laser beam before the first stop occurs". (b) Compute its expected value and variance