19. Partial Differential Equations

Try these first

1. 1.

   What is the probability of receiving exactly 2 emails in an hour if the average is 5?

   Hint

   Use the formula provided in class.

2. 2.

   Define λ in the context of Poisson distribution.

   Hint

   Think about what average means in statistics.

3. 3.

   What does the Poisson distribution model?

   • Continuous events in time
   • Discrete events in time or space
   • Events with a fixed outcome

   Hint

   Recall the basic definition we discussed.

4. 4.

   True or False: The mean and variance of a Poisson distribution are always equal.

   • True
   • False

   Hint

   Think back to the properties we just focused on.

5. 5.

   A hospital averages 10 patients arriving every hour. What is the probability that exactly 15 patients will arrive in the next hour?

   Hint

   Break it down using the PMF formula.

6. 6.

   In a factory, the average number of defects is 0.5 per item. If 100 items are produced, what is the likelihood of finding exactly 4 defects?

   Hint

   Consider what the average means in this scenario.