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_{c}. The Circle represents the entire area the cable station provides cable service for.

__Given:__Probability Distribution Function

P(r) = B if r <= r

_{c }(the person’s length is shorter than the radius of the cable station so they are in the circle)

P(r) = 0 if r > r

_{c }(the person’s length is longer than the radius of the cable station so they are outside the circle, hence distribution factor is 0)

B is a "normalization factor". B is chosen so that probability of finding a r in the circle is 1. For simplicity we have written P as a function of and not both r and θ. We must remember to perform all necessary integration over both r and θ.

We determine B by integrating P(r) from 0 to ∞ (over r) and from 0 to 2pi (over θ).

1 =∫

^{2π }∫

^{∞ }P(r)rdrdθ (I could not figure out how to put zeros under the integral symbols)

Using equations shown above for probability and integration

**Also what assumption can I make about the location of someone within that circle.**

__find an expression for B__.The function representing the cost of the person who is a cable user:

C(r) =λr where λ is a constant where r is the length from the person to the cable station.

and also C =∫

^{2π }∫

^{∞}C(r)P(r)rdrdθ (sorry did not know how to put 0 on the bottom of integrals)

I have to

**derive an**which represent the average cost for each cable station. Any Idea what C would be then? Thanks.

__expression for C__I was told to use ideas of integration and polar coordinates if I like to find the expressions.