Math Is Fun Forum

lucik1900

Member

Registered: 2013-03-15

Posts: 12

help me , this is a probability question.

You wish to fence off a rectangular paddock on one side of a river running through your property in a straight line. No fence is required along the side of the paddock formed by the river. The fence you will use is rolled up in a shed, and you are at the moment not quite sure how long it is. However, you are certain that it is between 3 and 5 km long, and your uncertainty regarding its length can be represented by a parabolic probability density function which tapers off to zero at 3 and 5 kms.

(a) Find and sketch the probability density function of Y, the area of the largest paddock you will be able to fence off.

(b) Find the expected value, mode and median of Y. Then illustrate these three quantities in the figure in (a).

Got an idea:

You require f(3) = f(5) = 0.

Therefore f(y) = a(y - 3)(y - 5).

Integrate f(y) from 3 to 5

Integrate and solve for a.

Once you have the pdf it is simple to calculate E(Y), mode and median.

?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me , this is a probability question.

Hi;

a) The sketch is below.

b) Mr F. got that idea first. As my neighbor says, "loooooking gooood maaaan." I agree so lets go with what Mr F. did.

After integrating,

So your PDF is

(-3/4)(y-3)(y-5)

Can you finish now? All you need to do is look at the graph and all questions can be answered.

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