Question 1159943
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Part a)


<font color=red size=4>The answer is 0.3</font> since we add the P(x) values when x is 4 or smaller, so when x = 2 or x = 4.


0.10+0.20 = 0.30 = 0.3


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Part b)


"x is greater than or equal to 2" is basically saying "every x value mentioned in the table" because x = 2 is the smallest item listed. 
Add up all the P(x) values. You should get 1 as the result. With any probability distribution, all the P(x) values must add to 1 to represent 100%.


<font color=red size=4>Answer = 1</font>


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Part c)


Make a column of the product of the X and P(X) values
<table border = "1" cellpadding = "5"><tr><td>X</td><td>P(X)</td><td>X*P(X)</td></tr><tr><td>2</td><td>0.1</td><td>0.2</td></tr><tr><td>4</td><td>0.2</td><td>0.8</td></tr><tr><td>6</td><td>0.3</td><td>1.8</td></tr><tr><td>8</td><td>0.4</td><td>3.2</td></tr></table>
Then add up the values in that new third column: 0.2+0.8+1.8+3.2 = 6


<font color=red size=4>Expected value = 6</font>


The expected value is another term for the mean.


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Part d)


Make yet another column. This time we'll represent the X^2*P(X) values
<table border = "1" cellpadding = "5"><tr><td>X</td><td>P(X)</td><td>X*P(X)</td><td>X^2*P(X)</td></tr><tr><td>2</td><td>0.1</td><td>0.2</td><td>0.4</td></tr><tr><td>4</td><td>0.2</td><td>0.8</td><td>3.2</td></tr><tr><td>6</td><td>0.3</td><td>1.8</td><td>10.8</td></tr><tr><td>8</td><td>0.4</td><td>3.2</td><td>25.6</td></tr></table>
Those new values add to: 0.4+3.2+10.8+25.6 = 40


Then we subtract off the square of the mean, or expected value, we got back in part c
40 - (mean)^2 = 40 - 6^2 = 40 - 36 = 4


<font color=red size=4>The variance is 4</font>


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Part e)


Apply the square root to the variance to get the standard deviation:
standard deviation = sqrt(variance)
standard deviation = sqrt(4)
<font color=red size=4>standard deviation = 2</font>
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