Probability, Distributions:

Let X be a discrete random variable that takes values in {2, 1, 0, 1, 2} each with the probability of 1/5 .

Also, Y is another discrete random variable defined as Y = X^2 .

1. Construct the joint probability distribution table.

2. Are X and Y independent? Justify.

3. Find Corr(X, Y ).

4. Based on your answer to part 2, can you explain the result in part 3?

Probability, Bayes' Theorem:

There is a corona virus test with 90% accuracy. Given that only 2% of the population is infected, answer the following questions.

1.What does it mean that the accuracy of the test is 90%?

2.If a person tests positive, what is the probability that the person actually has the disease.

3.What is the probability that a patient is misclassified?

4.If the person decides to repeat the test again (independent of the first one) what is the probability of being infected given that both tests are positive?

5.If the person decides instead of repeating the same test, he takes independently a cheaper test with accuracy of 80%. What is the probability of being infected given that both tests are positive?