**Learning Goal: **I’m working on a probability question and need guidance to help me learn.

1. Discrete Random Variables are random variables that can take on a finite or countable

distinct number of distinct values. Each value can be described by an integer value.

2. Continuous Random Variables are random variables that take an uncountably infinite

number of possible values, typically measurable quantities. The values are obtained by

measurement and may assume all values in the interval between any two given values along a

number line.

examples:

1. The number of arrivals at an emergency room between 6am and 12nn. DISCRETE

2. The weight of a box labeled as 20kg. CONTINUOUS

3. The number of kernel of popcorn in a container. CONTINUOUS

4. The number of applicants for a job. DISCRETE

5. The number of passenger in a jeepney. DISCRETE

6. The number of boys in a randomly selected three-child family. DISCRETE

7. The temperature of a cup of a coffee served at a restaurant. CONTINUOUS

8. The number of vehicles owned by a randomly selected household. DISCRETE

9. The air pressure of a tire on an automobile. CONTINUOUS

10.The average weight of a new born child in a certain hospital. CONTINUOUS

**Random Variables**

Random means are unpredictable. Hence, a random variable means a variable whose future value is unpredictable despite knowing its past performance

**Definition of a Random Variable**

A random variable is a variable whose possible values are the numerical outcomes of a random experiment. Therefore, it is a function which associates a unique numerical value with every outcome of an experiment. Further, its value varies with every trial of the experiment.

**Random Experiment**

Since random variables are outcomes of a random experiment, it is important to understand a random experiment as well. A random experiment is a process which leads to an uncertain outcome.

Usually, it is assumed that the experiment is repeated indefinitely under homogeneous conditions. While the result of a random experiment is not unique, it is one of the possible outcomes.

For example, when you toss an unbiased coin, the outcome can be a head or a tail. Even if you keep tossing the coin indefinitely, the outcomes are either of the two. Also, you would never know the outcome in advance.

In a random experiment, the outcomes are not always numerical. However, we need numbers as outcomes for calculations. Therefore, we define a random variable as a function which associates a unique numerical value with every outcome of a random experiment.

For example, in the case of the tossing of an unbiased coin, if there are 3 trials, then the number of times a ‘head’ appears can be a random variable. This has values 0, 1, 2, or 3 since, in 3 trials, you can get a minimum of 0 heads and a maximum of 3 heads.

**Types of Random variables**

We classify random variables based on their probability distribution. A random variable either has an associated probability distribution (Discrete Random Variable), or a probability density function (Continuous Random Variable). Therefore, we have two types of random variables – Discrete and Continuous.

**Discrete Random Variables**

Discrete random variables take on only a countable number of distinct values. Usually, these variables are counts (not necessarily though). If a random variable can take only a finite number of distinct values, then it is discrete.

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