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# S2 Continuous random variables watch

1. There is probably a really easy way to do this question but for some reason I really can't do it! Any help would be much appreciated
2. for part (a), you need to know what the area under this whole function should be.
You get then find the area in terms of a by finding the areas of the triangles and put this expression equal to what you know the total area has to be.

Finding the value of a makes it straightforward to use some coordinate geometry and find the equation of each part in (b).

For (c) note that half of the area must lie either side of the expected value.

For (d) you can use all of the information that you have found and recall that var(t)=integral(t^2 *f(t)) dt

The last part can be done by knowledge of a distribution and how this relates to s.deviation. Or, by knowing that variance=sd^2 and you know the variance from (d)
Hope this helps
3. (Original post by calla_lily)
...
(Original post by Barcelona'99)
For (c) note that half of the area must lie either side of the expected value.

For (d) you can use all of the information that you have found and recall that var(t)=integral(t^2 *f(t)) dt
For c) you need to consider the symmetry.

The fact that half the area lies on either side of the expected value is true in this case, and indeed for any symmetrical distribution, but it is NOT true in general.

Also, variance:

4. remember that integral of f(t) over 0 to 8 is equal to 2*integral from 0 to 4, (symmetry)
5. Thanks for the help guys

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Updated: November 24, 2013
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