17. A horizontal force acts on a crate whose weight is . The coefficient of static friction is . Determine the probability that the crate will slip. P and W are distributed independently.

Solution

Assume no slipping

From above two equations, we have

The maximum frictional force is

Thus, the distribution of the frictional force is and the distribution of the maximum frictional force is .

Then we construct function ,

Thus, the probability that the crate will slip is

Ans.