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# S1 WJEC 15th June 2016

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1. I don't get the questions involving integration, can someone help meee??

Thank you
2. Shoot.
3. (Original post by ovo_zverit)
I don't get the questions involving integration, can someone help meee??

Thank you
I've only started revising for this today but I think I know the questions you're on about. It's usually the last question on the paper about continuous random variables right?

So the probability density function , f(x) , is defined for a certain range of values. Eg: f(x) = x² +1 for 0 ≤ x ≤ 1
f(x) = 0 otherwise.

Since probabilities add to 1, if you sum every possible outcome between the given range, you will end up with one. This summation is done by integrating f(x) between the given range in the question. You will always be given this range in the question - you are usually asked to find/prove a certain value of k is correct, that makes up f(x).
Eg: f(x) = kx(x²+1) for 0≤x≤1

As mentioned earlier, this is done by integrating f(x) between the given range (0 to 1) and putting this integral equal to 1 (since probabilities add to 1). Hence k can be found.

The second place in the cumulative distribution questions where integrating is involved is to find E(X). The only difference here is you integrate "x f(x)" between the given range (not just f(x)).

Integration is also used to find the cumulative distribution function, F(x). This is slightly different to the other two types of integration, since we use a "dummy variable" when integrating.

To find F(x) we integrate f(x) between the lowest value of the range of f(x) (lower integral limit) and x (upper integral limit). As we are integrating up to a point x, it is bad practise to integrate the same variable. We therefore change f(x) to f(t) - this is done by simply changing all the x's to t's in the function.

The integration is then carried out as normal and the upper and lower limits are subbed into the equation. This results in the t's "disappearing" since they are replaced by the upper limit ,x, and whatever the lower limit is (usually 0).

Hope this helps , sorry if too much detail/didn't make sense but I'm not great at s1 myself either ahaha

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