5. Partial Differential Equations

Try these first

1. 1.

   Define sample space in your own words.

   Hint

   Think about all the results that can happen in an experiment.

2. 2.

   What is the formula for conditional probability?

   Hint

   Recall how two events relate in probability.

3. 3.

   What is Bayes' Theorem primarily used for?

   • To calculate averages
   • To update probabilities based on new evidence
   • To find maximum values

   Hint

   Think about how new information affects our beliefs.

4. 4.

   True or False: The prior probability is the updated probability after observing evidence.

   • True
   • False

   Hint

   Recall what happens before any evidence is considered.

5. 5.

   In a town, 2% of people have a rare disease. A test for this disease has a 98% true positive rate and a 10% false positive rate. If a randomly selected person tests positive, what is the probability they actually have the disease?

   Hint

   Break down the probabilities step-by-step to deduce the final probability.

6. 6.

   Explain the implications of using Bayes' Theorem in predicting stock market fluctuations. What would you need to consider?

   Hint

   Focus on how new information can shift market perceptions and probabilities.