Question 1206559
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X = number of children married people have
<table border = "1" cellpadding = "5"><tr><td>x</td><td>P(x)</td></tr><tr><td>0</td><td>0.15</td></tr><tr><td>1</td><td>0.20</td></tr><tr><td>2</td><td>0.35</td></tr><tr><td>3</td><td>????</td></tr><tr><td>4</td><td>0.10</td></tr><tr><td>5</td><td>0.05</td></tr><tr><td>6 (or more)</td><td>0.05</td></tr></table>
The two key rules for a probability distribution are:<ul><li>Each P(x) item must be between 0 and 1.</li><li>All of the P(x) values must add to 1.</li></ul>So,
P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 1
0.15+0.20+0.35+P(3)+0.10+0.05+0.05 = 1
0.9+P(3) = 1
P(3) = 1 - 0.9
P(3) = <font color=red>0.1</font>


The probability a married adult has exactly 3 kids is <font color=red size=4>0.1</font>


This is what the completed table will look like
<table border = "1" cellpadding = "5"><tr><td>x</td><td>P(x)</td></tr><tr><td>0</td><td>0.15</td></tr><tr><td>1</td><td>0.20</td></tr><tr><td>2</td><td>0.35</td></tr><tr><td>3</td><td><font color=red>0.10</font></td></tr><tr><td>4</td><td>0.10</td></tr><tr><td>5</td><td>0.05</td></tr><tr><td>6 (or more)</td><td>0.05</td></tr></table>


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Now to fill out the column labeled x*P(x).
As the name of this column suggests, we'll multiply each paired x and P(x) value.
Eg: 0*0.15 = 0 and 1*0.20 = 0.20
<table border = "1" cellpadding = "5"><tr><td>x</td><td>P(x)</td><td>x*P(x)</td></tr><tr><td>0</td><td>0.15</td><td>0</td></tr><tr><td>1</td><td>0.20</td><td>0.20</td></tr><tr><td>2</td><td>0.35</td><td>0.70</td></tr><tr><td>3</td><td>0.10</td><td>0.30</td></tr><tr><td>4</td><td>0.10</td><td>0.40</td></tr><tr><td>5</td><td>0.05</td><td>0.25</td></tr><tr><td>6 (or more)</td><td>0.05</td><td>0.30</td></tr></table>
The "6 (or more)" entry at the bottom is treated simply as x = 6. I wasn't sure how to handle that portion. 
Spreadsheet software is recommended. But since the table is fairly small, doing it by hand isn't that bad. 


Add up the values in the x*P(x) column to arrive at the <font color=red size=4>expected value 2.15</font>
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