Question

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is .

• A. 0.25

Answer 1

The correct option is A 0.25

Let x:the length of the shorter stick
P is the randomly chosen point.

Now 'x' is uniformly distributed between 0 to $\frac{1}{2}$ i.e. $xϵ[0,\frac{1}{2}]$

Then p.d.f. (Probability density function)

$f\left(x\right)=\frac{1}{(\frac{1}{2}-0)}=2$


So expected length is E(x)

$={\int }_0^{1/2}xf\left(x\right)dx$

$={\int }_0^{1/2}2xdx=\frac{1}{4}=0.25$