# STA257H1 : Summary notes

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You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

**Y=0 ** **Y=1**

X=0 |
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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?