本次加拿大代写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), find 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 coefficient Cor(X,Y ) = ρXY between X and Y .
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