Finding the Expected Value of Stick Breakage

[uva123]

Homework Statement

Suppose that a point is chosen at random on a stick that has length 15 inches, and that the stick is broken into two pieces at that point. Find the expected value of the lengths of the two pieces.

Homework Equations

E(x)=$$\sumf(x)xdx$$ from -infinity to +infinity (continuous case)
E(x)=$$\sumf(x)x$$ for all x (discrete case)

The Attempt at a Solution

X₁+X₂=15

PLEASE HELP!

 

[lanedance]

any ideas?

try starting from a single uniform random variable X, with uniform distribution, representing break distance from one end...

 

[jbunniii]

Start by defining a random variable X which represents the point where the stick is broken, measured from the left edge. What is E[X]?

Now define two random variables L and R, where L = length of the left piece, and R = length of the right piece.

Express L and R as functions of X. Then use that result to express E[L] and E[R] as functions of E[X].