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Simple pdf/cdf question... spot my mistake because I can't watch

1. Let's say

Then and .

Hence;

So, for our distribution function is

But apparently the answer is for .

2. Well , whereas what you've found is . You need to integrate between and (so you have to split the integral) and so on.
3. (Original post by nuodai)
Well , whereas what you've found is . You need to integrate between and (so you have to split the integral) and so on.
Why am I not considering both the parts of the cdf when and ?
4. (Original post by wanderlust.xx)
Why am I not considering both the parts of the cdf when and ?
I'm not really sure what you're asking. The question specifies that ; you could also work out the value of for if you wanted.

The value of is defined to be . Since the random variable can take any real value, we must have that . As we're told that we can rewrite this as , which is where the two different forms of for come in.
5. (Original post by nuodai)
I'm not really sure what you're asking. The question specifies that ; you could also work out the value of for if you wanted.

The value of is defined to be . Since the random variable can take any real value, we must have that . As we're told that we can rewrite this as , which is where the two different forms of for come in.
Yeah I just realised where I'm going wrong - for some reason my logic seems to think that must interfere somehow when calculating the CDF... when it really shouldn't do anything else other than change what PDF I'm integrating... yeah, that should be it. Cheers!
6. (Original post by wanderlust.xx)
Yeah I just realised where I'm going wrong - for some reason my logic seems to think that must interfere somehow when calculating the CDF... when it really shouldn't do anything else other than change what PDF I'm integrating... yeah, that should be it. Cheers!
Yup. I think your confusion was in thinking that meant that you had to consider too, when really what you need to do is find the probability that the random variable X (which can take any value, positive or negative) takes a value less than some specified positive number x.

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