6.1 Discrete Random Variables - Validity
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<p>You are given four probability distributions below. Determine which are valid.</p>
<table style="border-collapse: collapse; width: 100%;" border="1">
<caption>Possible Discrete Distributions for Understanding Check</caption>
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<tr>
<th style="width: 25%;" scope="col">
<p>Distribution 1</p>
</th>
<th style="width: 25%;" scope="col">
<p>Distribution 2</p>
</th>
<th style="width: 25%;" scope="col">
<p>Distribution 3</p>
</th>
<th style="width: 25%;" scope="col">
<p>Distribution 4</p>
</th>
</tr>
<tr>
<td style="width: 25%;">
<table style="border-collapse: collapse; width: 100%;" border="1" aria-label="Distribution 1">
<caption>Table 1</caption>
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<tr>
<th style="width: 50%; text-align: center;" scope="col">X</th>
<th style="width: 50%; text-align: center;" scope="col">P(X)</th>
</tr>
<tr>
<td style="width: 50%; text-align: center;">0</td>
<td style="width: 50%; text-align: center;">0.15</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">1</td>
<td style="width: 50%; text-align: center;">0.08</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">2</td>
<td style="width: 50%; text-align: center;">0.20</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">3</td>
<td style="width: 50%; text-align: center;">0.50</td>
</tr>
</tbody>
</table>
</td>
<td style="width: 25%;">
<table style="border-collapse: collapse; width: 100%;" border="1">
<caption>Table 2</caption>
<tbody>
<tr>
<th style="width: 50%; text-align: center;" scope="col">X</th>
<th style="width: 50%; text-align: center;" scope="col">P(X)</th>
</tr>
<tr>
<td style="width: 50%; text-align: center;">5</td>
<td style="width: 50%; text-align: center;">0.48</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">6</td>
<td style="width: 50%; text-align: center;">0.63</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">7</td>
<td style="width: 50%; text-align: center;">-0.36</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">8</td>
<td style="width: 50%; text-align: center;">0.25</td>
</tr>
</tbody>
</table>
</td>
<td style="width: 25%;">
<table style="border-collapse: collapse; width: 100%;" border="1">
<caption>Table 3</caption>
<tbody>
<tr>
<th style="width: 50%; text-align: center;" scope="col">X</th>
<th style="width: 50%; text-align: center;" scope="col">P(X)</th>
</tr>
<tr>
<td style="width: 50%; text-align: center;">0</td>
<td style="width: 50%; text-align: center;">0.01</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">1</td>
<td style="width: 50%; text-align: center;">0.02</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">2</td>
<td style="width: 50%; text-align: center;">0.97</td>
</tr>
</tbody>
</table>
</td>
<td style="width: 25%;">
<table style="border-collapse: collapse; width: 100%;" border="1">
<caption>Table 4</caption>
<tbody>
<tr>
<th style="width: 50%; text-align: center;" scope="col">X</th>
<th style="width: 50%; text-align: center;" scope="col">P(X)</th>
</tr>
<tr>
<td style="width: 50%; text-align: center;">0</td>
<td style="width: 50%; text-align: center;">2/3</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">1</td>
<td style="width: 50%; text-align: center;">1/12</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">2</td>
<td style="width: 50%; text-align: center;">1/6</td>
</tr>
<tr>
<td style="width: 50%; text-align: center;">3</td>
<td style="width: 50%; text-align: center;">1/8</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>