(Solved): Problem A1. (Discrete Joint Distribution) Grades in Calculus (X) and grades in etatistics (Y) are ...

Problem A1. (Discrete Joint Distribution) Grades in Calculus $$(X)$$ and grades in etatistics $$(Y)$$ are surveyed for 1000 students as follows. Let the values 1,2 , Determine the following. a. The joint probability distribution of $$X$$ and $$Y$$, i.e. $$f_{XY}(x,y)$$ b. $$P(X=1,Y?2)$$ c. The marginal probability distribution of $$X$$, i.e. $$f_X(x)$$ d. The mean of $$X$$, i.e. $$E[X]$$. e. The variance of $$X$$, i.e. $$V[X]$$. f. The conditional probability distribution of $$Y$$ given $$X=1$$, i.e. $$fY?X=1(y)$$ g. $$E[Y?X=1]$$ h. Are $$X$$ and $$Y$$ independent?