exercise:E28222568d: Difference between revisions

Latest revision as of 16:43, 19 June 2024

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

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]?

@@ Line 1: / Line 1: @@
-Assume that the random variables <math>X</math> and <math>Y</math> have the joint distribution given in [[guide:448d2aa013#table 4.5 |Table]].
+Assume that the random variables <math>X</math> and <math>Y</math> have the joint distribution given in [[#table 4.5 |Table]].
 <span id="table 4.5"/>
-{|class="table"
+{|class="table table-borderless"
 |+ Joint distribution.
 |-
 |||     ||  <math>Y</math>  ||       ||        ||
+|- style="border-bottom:solid 1px grey;"
+| ||     ||   -1  ||  0    ||  1     ||  2
 |-
-|||     ||   -1  ||  0    ||  1     ||  2
+|<math>X</math>
+| style="border-right:solid 1px grey"| -1
+|   0
+| 1/36
+|  1/6
+| 1/12
 |-
-|<math>X</math>  || -1  ||   0   || 1/36  ||  1/6   || 1/12
+|
+| style="border-right:solid 1px grey"| 0
+| 1/18
+|  0
+|  1/18
+|  0
 |-
-|||  0  || 1/18  ||  0    ||  1/18  ||  0
+|
+|style="border-right:solid 1px grey;"  |1
+|   0
+| 1/36
+|  1/6
+| 1/12
 |-
-|||  1  ||   0   || 1/36  ||  1/6   || 1/12
+|
-|-
+|style="border-right:solid 1px grey;" | 2
-|||  2  || 1/12  ||  0    ||  1/12  || 1/6
+| 1/12
+|  0
+|  1/12
+| 1/6
 |}