You-have-a-line-of-length-1-You-place-two-random-points-on-the-line-What-is-the-average-distance-between-the-two-points-Please-show-your-working-

Question Number 11095 by FilupS last updated on 12/Mar/17

You have a line of length 1 .

You place two random points on the line .

What is the average distance between

the two points ? Please show your working .

Commented by FilupS last updated on 12/Mar/17

For context, the answer is \frac{1}{3}

Answered by ajfour last updated on 12/Mar/17

\frac{1}{4} .

Commented by FilupS last updated on 12/Mar/17

incorrect

please show working .

it helps to see mistakes, etc .

Commented by ajfour last updated on 12/Mar/17

{\int_{0}}^{1} {\frac{\int_{x}^{1} (y - x) d y}{1 - x}} d x

Commented by FilupS last updated on 12/Mar/17

Please explain where you derived

this result ?

Answered by ajfour last updated on 12/Mar/17

\int_{0}^{1} \int_{0}^{1} ∣ y - x ∣ d y d x = \frac{1}{3} .

h e l p i n t e r p r e t i n g!

Commented by FilupS last updated on 12/Mar/17

Although this gives the correct solution,

I am unsure that this is a correct method

of approaching the problem .

The method I am aware of is via

probability density

Commented by FilupS last updated on 12/Mar/17

please tell me how you got to

this result

Commented by ajfour last updated on 12/Mar/17

Commented by FilupS last updated on 12/Mar/17

Although you have gotten the same result,

i think you have solved for a similar

question where (x, y) \to R^{2}

I beleive this question has (x, y) \to R^{1}

I honestly {don}^{'} t know

The method I am looking for has to do

with probability

Commented by ajfour last updated on 12/Mar/17

y o u c a n, a s a s e p a r a t e m a t t e r

v i e w m y p r o o f t o Q . 11036 .

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