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 February 23rd, 2013, 02:35 AM #1 Member   Joined: Dec 2011 Posts: 61 Thanks: 0 statistics uniform continuous distribution I get confused about this question.please help me. A rectangle has a perimeter of 20cm. The length,x 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. Can anyone show and explain the solution. In the mark scheme we use Y~U[3,9]. Why is it so?? Please help me.
February 23rd, 2013, 09:39 AM   #2
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Re: statistics uniform continuous distribution

Quote:
 Originally Posted by najaa Can anyone show and explain the solution. In the mark scheme we use Y~U[3,9]. Why is it so?? Please help me.
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Perimeter=2X+2Y=20 so ?+?=10 and Y=10-X which means that since X~U(1,7) that means that Y~U(10-7,10-1)=U(3,9).

The probability you ask is $\mathbb{P}\left(\mathbb{X}=>5\right)+\mathbb{P}\lef t(\mathbb{Y}=<5\right)=\frac{7-5}{6}+\frac{5-3}{6}=\frac{2}{3}$.

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