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elixir [45]
3 years ago
6

A stick is broken into two pieces, at a uniformly random break point. Find the CDF and average of the length of the longer piece

.
Mathematics
1 answer:
Oksanka [162]3 years ago
5 0

Answer:

P(L ≤ l) =P (1-l ≤ U ≤ l)= l- ( 1 - l ) = 2 l - 1

Step-by-step explanation:

let assume that stick has length 1.Random variable L that make length of a longer piece and random variable U that mark point .See that L < l means that

U≤ l and 1-U ≤l

P(L ≤ l) =P (1-l ≤ U ≤ l)= l- ( 1 - l ) = 2 l - 1

this means 1-l≤U≤l

so we have

if we have L  [1/2,1]

then apply the formula we have E(L)=3/4

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Look at the graph picture I attached

y = mx + c

c is the intercept, which is why the graph crosses the y-axis at +3

to find where it crosses the x-axis, we make y = 0

y = 0\\\to -\frac{2}{3}x + 3 = 0\\-\frac{2}{3} = -3\\\frac{2}{3}x = 3\\2x = 9\\x = \frac{9}{2}\ \ (=4.5)

8 0
2 years ago
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In conclusion, we have:  

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3 years ago
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Ainat [17]
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