exercise:E28222568d: Difference between revisions
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Assume that the random variables <math>X</math> and <math>Y</math> have the joint distribution given in [[#table 4.5 |Table]]. | |||
given in [[ | |||
<span id="table 4.5"/> | <span id="table 4.5"/> | ||
{|class="table" | {|class="table table-borderless" | ||
|+ Joint distribution. | |+ Joint distribution. | ||
|- | |- | ||
||| || <math>Y</math> || || || | ||| || <math>Y</math> || || || | ||
|- style="border-bottom:solid 1px grey;" | |||
| || || -1 || 0 || 1 || 2 | |||
|- | |- | ||
||| | |<math>X</math> | ||
| style="border-right:solid 1px grey"| -1 | |||
| 0 | |||
| 1/36 | |||
| 1/6 | |||
| 1/12 | |||
|- | |- | ||
| | | | ||
| style="border-right:solid 1px grey"| 0 | |||
| 1/18 | |||
| 0 | |||
| 1/18 | |||
| 0 | |||
|- | |- | ||
||| | | | ||
|style="border-right:solid 1px grey;" |1 | |||
| 0 | |||
| 1/36 | |||
| 1/6 | |||
| 1/12 | |||
|- | |- | ||
| | | | ||
|- | |style="border-right:solid 1px grey;" | 2 | ||
| 1/12 | |||
| 0 | |||
| 1/12 | |||
| 1/6 | |||
|} | |} | ||
<ul><li> What is <math>P(X \geq 1\ \mbox {and\ } Y \leq 0)</math>? | |||
<ul style="list-style-type:lower-alpha"><li> What is <math>P(X \geq 1\ \mbox {and\ } Y \leq 0)</math>? | |||
</li> | </li> | ||
<li> What is the conditional probability that <math>Y \leq 0</math> given that <math>X = 2</math>? | <li> What is the conditional probability that <math>Y \leq 0</math> given that <math>X = 2</math>? | ||
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.
| [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]?