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# S2 Uniform distrib question watch

1. I don't have the solution to this question, neither do I know where it came from but was wondering if I was doing it right. I hate stats :|

"A rectangle has a perimeter of 20cm. The length, Xcm, of one side of this rectangle is uniformly distributed between 1cm and 7cm.

Find the probability that the length of the longer side of the rectangle is more than 6cm long. (5 marks)"
2. If you draw the rectangle out, you should be able to convince yourself that when X = 1, the 'longer' side is (20-2)/2 = 9, and when X = 7, the 'longer' side is 3. As these are the two extremes, the longer side is distributed uniformly in the interval (3,9). The probability that it is greater than 6 is then easy to calculate.
3. (Original post by Dream Eater)
If you draw the rectangle out, you should be able to convince yourself that when X = 1, the 'longer' side is (20-2)/2 = 9, and when X = 7, the 'longer' side is 3. As these are the two extremes, the longer side is distributed uniformly in the interval (3,9). The probability that it is greater than 6 is then easy to calculate.
Thanks, I understand that much except I tried the reverse (I think). I tried the probability that the shorter side is less than 4.
Attempting to draw this out as a distribution function ( I have no idea what I'm doing) I found the probability at any length between 1cm and 7cm to be 1/6 ? Then 3x 1/6 = 0.5 ? But I'm not sure this is correct since what happens to the probability of < 1cm?

Help ?
4. (Original post by CynicaL)
Help ?
I think this has gone off track so here's my version of the solution:

Spoiler:
Show

One side is uniformily distributed between 1 and 7 cm; lets call this side A.

The sum of two adjacent sides is 10, (half the perimeter).

A will be the longer side if A is greater than 5 (half of 10), and it will be greater than 6 if A lies between 6 and 7.

The other side will be the longer side if A is less than 5. And that side will be longer than 6 if A is less than 4, that is if A lies between 1 and 4.

So the longer side will be greater than 6, if A lies between 1 and 4 or between 6 and 7.

Probability is [(4-1) + (7-6)] / (7-1) =2/3.

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Updated: December 12, 2010
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