Theory. Distribution law of a two-dimensional discrete random vector in a tabular form; independent random variables, interpretation of correlation coefficient value (are random variables correlated?). 1. Discrete random vector law is given. Check if variables are independent. -1 0.2 0.3 0.1 0.4 2. Which statement is true? a) If the variables are independent, they are uncorrelated (correlation coefficient is o). b) If correlation coefficient is O, the variables are independent.
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You are given a fair die, i.e. the outcomes of any throw are contained in the sample space 
(a) Derive the joint pdf of X and Y. Provide this in the form of a table
Y=0 Y=1
| X=0 | ||
| X=1 |
b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?
