Answer to Question #307746 in Statistics and Probability for ash

Question

1. How do you describe a discrete random variable? Give examples.

2. How do you describe a continuous random variable? Give examples.

3. What are the properties of a probability distribution?

Answer 1

1. Discrete random variables can take on either a finite or at most a countably infinite set of discrete values (for example, the integers).

Examples of discrete random variables include the values obtained from rolling a die and the grades received on a test out of 100.

2. Continuous random variables, on the other hand, take on values that vary continuously within one or more real intervals, and have a cumulative distribution function (CDF) that is absolutely continuous. As a result, the random variable has an uncountable infinite number of possible values, all of which have probability 0, though ranges of such values can have nonzero probability.

Selecting random numbers between 0 and 1 are examples of continuous random variables because there are an infinite number of possibilities.

3. The main properties of a probability distribution are the mean and the variance.

The mean is the average of a group of numbers, and the variance measures the average degree to which each number is different from the mean.