Find the probability that a randomly chosen point is the left part of the interval:

Find the probability that two randomly selected points on a circle create an angle less than

:

Generate a uniform distribution of points on a circle:

Obtain a random number from the inverse CDF of a distribution:

The nozzle of a fountain shoots water at speed

and angle

varying between

and

with equal probability. Find the expected horizontal distance where water touches the ground:

The phase angle

of a sinusoidal signal is uniformly distributed from

to

. Find the probability that

is between

and

:

Find the probability that the phase angle is at most

:

Find the average value of

:

Find the probability that

is within one standard deviation from the average value:

Two trains arrive at a station independently and stay for 10 minutes. If the arrival times are uniformly distributed, find the probability the two trains will meet at the station within one hour:

The region where the two trains meet:

Shafts are produced with their diameter

following uniform distribution over

independently of the production of shaft housings, the inner diameter

of which follows uniform distribution over

. Given that the optimal difference between the diameters is up to

, find the probability that a shaft will fit into a housing:

Show the shafts in blue and holes in pink:

The lifetime of a device has uniform distribution. Find the reliability of the device:

The hazard function increasing in time:

Find the reliability of two such devices in a series:

Find the reliability of two such devices in parallel:

Compare the reliability of both systems for

and

:

Show a distribution function and its histogram in the same plot:

Compare the PDF to its histogram version:

Compare the CDF to its histogram version: