Boundaries of CRV's Watch

jamiescriven
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For CRV's, does the range have to be in the form of 'less and or equal to'? So would the boundaries need to be changed into the new boundaries as shown in the image.
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Zacken
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(Original post by jamiescriven)
S1 WJEC Topic
For CRV's, does the range have to be in the form of 'less and or equal to'? So would the boundaries need to be changed into the new boundaries as shown in the image.
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No, no, no! You're thinking of a discrete distribution. 5 < x < 10 says precisely what it needs to say, you can't really change that.

If you say 4 \leq x \leq 9 then what about x=4.1, 4.5, 9.25, 9.9? You're throwing a ****-ton of values away that will get you the wrong answer.

What is wrong with having 5<x<10? If your concern is integration then for a continuous random variable (due to the measure of the set (I think, somebody correct me)) we have:

F(X) = \int_5^{10} f(x) \, \mathrm{d}x for both 5 < x < 10 and 5 \leq x \leq 10.
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jamiescriven
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Oh yeah, thanks a lot!
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Zacken
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(Original post by jamiescriven)
Oh yeah, thanks a lot!
No problem!
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