Here are some statistical and probabilistic statements. However
reasonable they might sound, they CANNOT be completely true, or
might even be completely false. They are, at best, an
approximation, although the approximation might be very good.
- I toss a coin. The chance of landing heads is $1$ minus the
chance of landing tails.
- The energy of a randomly selected atom in a box is normally
distributed with some mean and variance.
- My pdf is a semi-circle of radius 1.
- For any piece of uranium, half of the mass will decay every
time the half-life elapses.
- I record the time of day at which an event occurs, with the
knowledge that the event is just as likely to occur at any time as
any other. The time measured will be a $U(0,1)$ random
- An influenza pandemic is just as likely to occur one year as
- The arithmetic mean of the number of children per
family in a certain population is $a$. Therefore, the arithmetic
mean of the number of siblings each child has is $a-1$.
- The expected age of death of a randomly selected $40$ year old
is the same as the expected age of death of a randomly selected
$35$ year old.
Can you invent your own statistical statements which sound
plausible but must be false?