1. Math
  2. Statistics And Probability
  3. problem 3 let a be a quotrandom pointquot that coincides...

Question: problem 3 let a be a quotrandom pointquot that coincides...

Question details

Problem 3 Let A be a random point that coincides with the point a1,a2,as or as with equal probabil- ities. d4 Let a random variable X be the first coordinate of the point A, a random variable Y be the scond coordinate of the point A. (a) Find the joint distribution of random variables X and yY (b) Find the marginal distribution of X and Y. (c) Find the cumulative distribution functions of X and Y (d) Compute E(X] and E (e) Compute Var[X], VarlY], Cor(X, Y), Corr(x, Y). (f) Find the conditional distribution of Y given X =-1,0,1. (g) Compute ElYlXe-1], ElYIX-0), ElYlX = 11. (h) Characterize a random variable E[YJx]. 6) Verify the Law of Iterated Expectations by checking EY]- ELEYIXI G) Is the point with coordinates (EIX], E[Y]) in the support of A? (k) Are the random variables X and Y correlated? Independent? Discuss. (1) What would the joint distribution be if the random variables X and Y are independent and their marginal distributions do not change.
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution