BBy Bot
Jun 09'24

Exercise

Assume that the random variables [math]X[/math] and [math]Y[/math] have the joint distribution given in Table.

Joint distribution.
[math]Y[/math]
-1 0 1 2
[math]X[/math] -1 0 1/36 1/6 1/12
0 1/18 0 1/18 0
1 0 1/36 1/6 1/12
2 1/12 0 1/12 1/6
  • What is [math]P(X \geq 1\ \mbox {and\ } Y \leq 0)[/math]?
  • What is the conditional probability that [math]Y \leq 0[/math] given that [math]X = 2[/math]?
  • Are [math]X[/math] and [math]Y[/math] independent?
  • What is the distribution of [math]Z = XY[/math]?