<PRE><B>Question 1192780</B>
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Given Table
&lt;table border = &quot;1&quot; cellpadding = &quot;5&quot;&gt;&lt;tr&gt;&lt;td&gt;X&lt;/td&gt;&lt;td&gt;-2&lt;/td&gt;&lt;td&gt;-1&lt;/td&gt;&lt;td&gt;0&lt;/td&gt;&lt;td&gt;1&lt;/td&gt;&lt;td&gt;2&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;P(X)&lt;/td&gt;&lt;td&gt;1/8&lt;/td&gt;&lt;td&gt;2/8&lt;/td&gt;&lt;td&gt;2/8&lt;/td&gt;&lt;td&gt;2/8&lt;/td&gt;&lt;td&gt;1/8&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;


The notation P(X ≤ 2) means &quot;The probability X ≤ 2 occurs&quot;
This means X = 2 or X &lt; 2.
As the table shows, the largest item is X = 2 itself, meaning that X ≤ 2 encompasses all possible outcomes. Therefore, we have 100% probability that X ≤ 2 happens.
We write P(X ≤ 2) = &lt;font color=red&gt;1&lt;/font&gt;
Note that all the fractions add to: 1/8+2/8+2/8+2/8+1/8 = (1+2+2+2+1)/8 = 8/8 = 1.


P(X &gt; -2)  = &lt;font color=red&gt;7/8&lt;/font&gt; because P(X = -2) = 1/8, so being larger than -2 will have a probability of 1 - 1/8 = 7/8.
Or you could add up all the P(x) values for X = -1 all the way up to X = 2.


P(-1 ≤ X ≤ 1) = P(-1) + P(0) + P(1)
P(-1 ≤ X ≤ 1) = 2/8 + 2/8 + 2/8
P(-1 ≤ X ≤ 1) = (2+2+2)/8
P(-1 ≤ X ≤ 1) = 6/8
P(-1 ≤ X ≤ 1) = &lt;font color=red&gt;3/4&lt;/font&gt;


P(X ≤ -1) = P(-2) + P(-1)
P(X ≤ -1) = 1/8 + 2/8
P(X ≤ -1) = 3/8
P(X ≤ -1 or X = 2) = P(X ≤ -1) + P(X = 2)
P(X ≤ -1 or X = 2) = 3/8 + 1/8
P(X ≤ -1 or X = 2) = 4/8
P(X ≤ -1 or X = 2) = &lt;font color=red&gt;1/2&lt;/font&gt;


This is a discrete probability distribution with X only able to take on the values from the set {-2, -1, 0, 1, 2}
Something like X = 1.15 is not possible. 
Saying X ≤ 1.15 is the same as X ≤ 1 because X = 1 satisfies the requirements that X = 1.15 or X &lt; 1.15.
So P(X ≤ 1.15) = P(X ≤ 1) = &lt;font color=red&gt;7/8&lt;/font&gt; which can be found by adding every P(X) value from x = -2 on up to x = 1; or take the shortcut 1 - P(2) = 1 - 1/8 = 7/8.


P(X ≤ 2.2) = P(X ≤ 2) = &lt;font color=red&gt;1&lt;/font&gt; for similar reasoning as mentioned earlier.


P(-1.1 &lt; X ≤ 1) = P(-1 &lt; X ≤ 1) 
P(-1.1 &lt; X ≤ 1) = &lt;font color=red&gt;3/4&lt;/font&gt; also found earlier



P(X &gt; 0) = P(X ≥ 1)
P(X &gt; 0) = P(1) + P(2)
P(X &gt; 0) = 2/8 + 1/8
P(X &gt; 0) = &lt;font color=red&gt;3/8&lt;/font&gt;


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Answers:


Part 1
(a)P(X ≤ 2) = &lt;font color=red&gt;1&lt;/font&gt;
(b)P(X &gt; -2) = &lt;font color=red&gt;7/8&lt;/font&gt;
(c)P(-1 ≤ X ≤ 1) = &lt;font color=red&gt;3/4&lt;/font&gt;
(d)P(X ≤ -1 or X=2) = &lt;font color=red&gt;1/2&lt;/font&gt;


Part 2
(a)P(X ≤ 1.15) = &lt;font color=red&gt;7/8&lt;/font&gt;
(b)P(X ≤ 2.2) = &lt;font color=red&gt;1&lt;/font&gt;
(c)P(-1.1 &lt; X ≤ 1) = &lt;font color=red&gt;3/4&lt;/font&gt;
(d)P(X &gt; 0) = &lt;font color=red&gt;3/8&lt;/font&gt;
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