Need help, Expections and Joint Dist. Question


I have been stuck on the following past paper question for the past week and still have not been able to find an answer. It is broken down into part A, B and C. If anyone is able to answer this question with explanation I will be eternally grateful.

Let X and Y be discrete random variables whose possible values are X=0 and 10, and Y= -20 and 10. The joint distribution of (Y,X) depends on the unknown parameter c. The probabilities of the possible values are given in the cells of the following table:

------- Y = -20 ¦ Y = 10
X = 0 ¦ 0.15 + c ¦ 0.3
X =10¦ 0.35 - c ¦ 0.2

qa) You know that E(4X+Y)=13. What is the value of c?
qb) Calculate E(Y|X=0) and E(Y|X=10) (Understand this part)
qc) c) Consider a linear regression model: Y=B0 + B1X + U. with E(u¦ X) = 0 Using the joint
distribution of (Y,X) given above, what is the value of B0 and B1 in this model.

(B0 and B1) are the slope and intercept coefficients of the linear regression. real symbol Beta wouldn't type.

Any help will be hugely appreciated.
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