Please help, tutors can't even help me lol

[name14]

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Solved outside.

 

[Deleted member 4993]

The distance of someone from the center of a circle to outside the circle (a cable station) is depicted as r, and the regular radius of that circle(the cable station) is depicted as r_c.

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 =₀∫^2π ₀∫^∞ P(r)rdrdθ (I could not figure out how to put zeros under the integral symbols)

Using equations shown above for probability and integration find an expression for B. Also what assumption can I make about the location of someone within that circle.
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> =₀∫^2π ₀∫^∞C(r)P(r)rdrdθ (sorry did not know how to put 0 on the bottom of integrals)

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

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

Put the 'zero' as subscript.



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[daon2]

The distance of someone from the center of a circle to outside the circle (a cable station) is depicted as r, and the regular radius of that circle(the cable station) is depicted as r_c.

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 find an expression for B. Also what assumption can I make about the location of someone within that circle.
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 expression for C which represent the average cost for each cable station. Any Idea what C would be then? Thanks.

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

This question is not exactly clear. What is the difference between C and <C>?

Also what assumption can I make about the location of someone within that circle. - How would we know? Assumptions should be supplied with the problem.

B is chosen so that probability of finding a r in the circle is 1. - What is "a r"

I was told to use ideas of integration and polar coordinates if I like to find the expressions. - If you like? Well the entire problem looks to already be in terms of polar coordinates.

 

[name14]

Solved outside

 

[HallsofIvy]

You still haven't answered the crucial question, "what assumption can I make about the location of someone within that circle." Are we to assume that all possible points in the circle are equally likely to be locations?

 

[name14]

Solved outside