- #1
Ackbach
Gold Member
MHB
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Here is this week's POTW, a problem submission by Track. Thanks, Track!
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I thought y'all could use some more stochastic love. Requires knowledge of calculus-based probability theory.
Suppose a $12$-inch, uniformly-shaped wooden stick is held securely at both ends, such that the stick does not move. The stick is then subjected to significant pressure until it snaps cleanly. Let $X$ be the distance from the left end of the stick at which the break occurs. The probability density function of $X$ is given by:
$$f_X(x)=\left\{\begin{array}{rl}
\left(\dfrac{x}{24}\right)\left(1-\dfrac{x}{12}\right), & 0\le x \le 12 \\
0, & \text{otherwise}
\end{array}\right.$$
What is the expected length of the shorter segment when the stick snaps?
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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I thought y'all could use some more stochastic love. Requires knowledge of calculus-based probability theory.
Suppose a $12$-inch, uniformly-shaped wooden stick is held securely at both ends, such that the stick does not move. The stick is then subjected to significant pressure until it snaps cleanly. Let $X$ be the distance from the left end of the stick at which the break occurs. The probability density function of $X$ is given by:
$$f_X(x)=\left\{\begin{array}{rl}
\left(\dfrac{x}{24}\right)\left(1-\dfrac{x}{12}\right), & 0\le x \le 12 \\
0, & \text{otherwise}
\end{array}\right.$$
What is the expected length of the shorter segment when the stick snaps?
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!