How to do radiometric dating problems
So clearly, to describe the probability of hitting this board’s points, it is not sufficient to consider only the probability of each individual point being hit, but rather we have to consider how likely we are to hit various regions of the board, such as the region constituting the bullseye.
Even though each particular point has a zero probability of being hit, define probabilities on an infinite set, though as the Gaussian distribution case shows, we may have to actually let the probabilities be assigned to subsets of our original set, rather than to every object in the set itself.
Well, each integer can be thought of as having an infinite sequence of zero digits to the left of its first non-zero digit.
This algorithm will have a probability of 0 of producing a number with an infinite successive sequence of zeros, and therefore will have a zero probability of producing an integer!
Strictly speaking, it assigns a probability of zero to each of the individual real numbers, but assigns a non-zero probability to subsets of real numbers.
For example, if we sample from a Gaussian distribution, there is a formula that can tell us how likely the number is to be less than any particular value X (so the set of all numbers less than X is assigned a positive probability).
But, if the number cannot be transmitted, no computer could ever make a copy of it, which implies that no computer could ever generate such a number.
does a uniform distribution on the integers exist)? A probability mass function (which is the kind of probability distribution we need in this case) is defined to be a positive function that has a sum of values equal to 1.
But any positive function that assigns an equal value to each integer must have probabilities that sum to either infinity or zero, so the desired distribution is impossible to construct.
For real numbers between 0 and 1, we can use the following sampling procedure: i. Set the nth digit of our number after the decimal point to a random number from 0 to 9. Essentially we are just constructing a number by choosing each of it’s decimal digits randomly. when it DOES produce integers those integers are each equally likely).
But what if we wanted to carry out this procedure for the set of all integers? But the algorithm does not actually do what we would like.