Require assistance with the below math questions, please.

1)

Probability, Distributions: Let X be a discrete random variable that takes values in {-2, -1, 0, 1, 2} each with the probability of . Also, Y is another discrete random variable defined as Y = X2. (i) Construct the joint probability distribution table. (ii) Are X and Y independent? Justify. (iii) Find Corr(X, Y). (iv) Based on your answer to part (b), can you explain the result in part (c)?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. {i} 'What does it mean that the accuracy of the test is Q'ii}? {ii} If a person tests positive, what is the probability that the person actually has the disease. {iii} What is the probability that a patient is missclassied'? {iv} [f the person decides to repeat the test again {independent of the rst one] what is the probability of being infected given that both tests are positive? {v} [f the person decides instead of repeating the same test, he takes independently a cheaper test with accuracy of 30%. What is the probability of being infected given that both tests are positive? Probability, Distributions: Let X be a continuous random variable with a probability density function given by f(x) = 0 otherwise (i) Find the value of k. (ii) Calculate P(X