Does Sumi break the stick? (into statement)
Answers
Answer:
This Take a one-foot stick,lay it down, and you simultaneously cut it at two points in order to get three pieces. It is equivalent to choose two points X and Y on the stick.
From left to right, the first piece A will be of size the minimum between X and Y minus 0.
The piece on the right will be of size 1 minus the maximum between X and Y, or 1−B where B=max(X,Y)
The one in the middle is of size X−Y fs X>Y, or Y−X if X≤Y, in other words , |X−Y|=B−A
Finally, C is the longest stick, that is max(A,1−B,B−A)
The cdf is then defined as follows
FC(a)=P(C≤a)=P(max(A,1−B,B−A)≤a)
If the maximum between A,1−B and B−A is smaller than a, therefore each of them are smaller than a, and reciprocally.
We can rewrite the cdf as
FC(a)=P(C≤a)=P(A≤a,1−B≤a,B−A≤a)
X and Y are totally symmetrical, you can write
P(A≤a,1−B≤a,B−A≤a)=P(A≤a,1−B≤a,B−A≤a,X<Y)+P(A≤a,1−B≤a,B−A≤a,X≥Y)
Thus,
P(A≤a,1−B≤a,B−A≤a)=2P(X≤a,1−Y≤a,Y−X≤a,X<Y)
A bit of geometry will give you the result : draw a square [0,1]∗[0,1], the vertical line {x=a}, the horizontal line {y=1−a}, the straight lines y=a+x and y=x. Locate the intersection of the surfaces defined by P(A≤a,1−B≤a,B−A≤a) and you will get the results.
Answer:
Sumi Break sticks.
Explanation:
Mark me the Brain Liest