Question

A measurable quantity which takes any numerical value with in certain limit is ________.

Answer 1

Dear student,

(In the context of probability)

In probability and statistics, a random variable is a variable whose possible values are outcomes of a random phenomenon.

As a function, a random variable is required to be measurable, which rules out certain pathological cases where the quantity which the random variable returns is infinitely sensitive to small changes in the outcome.

Explanation

It is common that these outcomes depend on some physical variables that are not well understood. For example, when tossing a fair coin, the final outcome of heads or tails depends on the uncertain physics. Which outcome will be observed is not certain.

The coin could get caught in a crack in the floor, but such a possibility is excluded from consideration. The domain of a random variable is the set of possible outcomes. In the case of the coin, there are only two possible outcomes, namely heads or tails. Since one of these outcomes must occur, either the event that the coin lands heads or the event that the coin lands tails must have non-zero probability.

Regards