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这是一篇加拿大作业是关于概率学限时测试
Examination aids allowed: Open notes-books
Instructions:
Read the questions carefully and answer only what is being asked.
Answer all questions directly on the examination paper; use the last pages if you need more space, and provide clear pointers to your work.
Show your intermediate work, and write clearly and legibly.


2. (20 points) Consider two random variables X and Y that are binary valued, i.e., the set of possible values is {0,1}. Let the marginal distribution of X be

It is given that the conditional distribution of Y given X is

(a) (10 points) Find the value of p ∈ [0,1] such that the marginal distributions of X and Y are the same.
(b) (10 points) For the value of p given in (a), nd the conditional distribution of X given Y .

3. (20 points) Let (X,Y ) be a random vector whose distribution is given by
(a) (4 points) Find the marginal distributions of X and Y , and give their name and parameters.
(b) (16 points) Find the correlation coecient Cor(X,Y ) = ρXY between X and Y .