4. Let Y be a random variable wit ven in the table below. y 1 2 3 4 p(y) 0.4 0.3 0.2 0.1 (a) Plot the probability distribution with y on the horizontal axis and p(y) on the vertical axis. (b) Find E[Y], E[1/Y] and V(Y).
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Use your Probability knowledge to fill the blanks in the table below.
| P(A) | P(B) | Conditions for Events A and B | P(A |
 |
 |
|
| (a) | 0.3 | 0.4 | Mutually Exclusive | 0.7 | 0 | |
| (b) | 0.3 | 0.4 | Independent | |||
| (c) | 0.1 | 0.5 | 0.6 | |||
| (d) | 0.2 | 0.5 | 0.1 |
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?
