Introduction to Random Variables

A random variable is:

• a deterministic value

• a variable that can take on different values randomly

• a fixed number

• a constant value

Statistics is the study of:

• numbers and data analysis

• historical events

• chemical reactions

• literary works

What is probability?

• Probability is a measure of the likelihood of an event occurring.

• Probability is a type of mathematical operation.

• Probability is a measure of certainty.

• Probability is a type of statistical data.

The probability distribution function (PDF) for discrete random variables is:

• A function that assigns probabilities to each possible outcome.

• A function that integrates to one over the entire space.

• A function that describes the likelihood of a continuous random variable.

• A function that is always non-negative.

The cumulative distribution function (CDF) for discrete random variables is:

• A function that assigns probabilities to each possible outcome

• A function that gives the probability that a random variable is less than or equal to a certain value

• A function that describes the likelihood of a random variable taking on a specific value

• A function that provides the expected value of a random variable

Describe the mean, variance, and standard variation for discrete random variables.

• The mean is the average value, variance measures the spread, and standard deviation is the square root of variance.

• The mean is the sum of all values, variance is the difference between highest and lowest values, and standard deviation is the variance squared.

• The mean is the middle value, variance is the average of squared differences from the mean, and standard deviation is the variance cubed.

• The mean is the most frequent value, variance is the range of values, and standard deviation is the variance divided by the mean.

The probability density function (PDF) for continuous random variables is used to:

• Determine the probability of a random variable taking on a specific value.

• Calculate the cumulative distribution function (CDF).

• Describe the likelihood of a random variable falling within a particular range of values.

• Find the expected value of a random variable.

The cumulative distribution function (CDF) for continuous random variables is:

• a function that assigns probabilities to intervals

• a function that assigns probabilities to individual outcomes

• a function that assigns probabilities to discrete events

• a function that assigns probabilities to random variables

We learn probability because:

• it helps us make informed decisions based on likelihoods.

• it is a branch of mathematics that deals with numbers.

• it is a historical subject with no practical use.

• it is only used in gambling.

The theory of probability helps quantify:

• certainty

• uncertainty

• exact outcomes

• deterministic events