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- In the ``game'' of Russian roulette, the player inserts a single cartridge into the drum
of a revolver, leaving the other five chambers of the drum empty. The player then spins
the drum, aims at his/her head, and pulls the trigger.
- What is the probability of the player still being alive after playing the game times?
- What is the probability of the player surviving turns in this game, and then being
shot the th time he/she pulls the trigger?
- What is the mean number of times the player gets to pull the trigger?

- Suppose that the probability density for the speed of a car on a road
is given by

where
. Here, and are positive constants. More
explicitly, gives the probability that a car has a speed
between and .
- Determine in terms of .
- What is the mean value of the speed?
- What is the ``most probable'' speed:
*i.e.*, the speed
for which the probability density has a maximum?
- What is the probability that a car has a speed more than three times as large
as the mean value?

- An radioactive atom has a uniform decay probability per unit time :
*i.e.*, the probability of decay in a time interval is .
Let be the probability of the atom not having decayed at time ,
given that it was created at time . Demonstrate that

What is the mean lifetime of the atom?

** Next:** Wave-Particle Duality
** Up:** Continuous Probability Distributions
** Previous:** Continuous Probability Distributions
Richard Fitzpatrick
2010-07-20