Data Science and Machine Learning (Theory and Projects) A to Z - Random Variables: Bernulli Random Variables

The video introduces random variables, focusing on discrete random variables and the probability mass function (PMF). It explains the concept of countable values and provides examples, including the sum of dice rolls and coin tosses. The video also introduces the Bernoulli random variable, highlighting its simplicity and applications in logistic regression. The PMF is described as a probability model for discrete variables, adhering to probability laws and axioms.

What is a discrete random variable?

• A variable that can only take integer values

• A variable with a countable number of possible values

• A variable that is always finite

• A variable with an uncountable number of possible values

Which of the following is true about discrete random variables?

• They are always finite

• They cannot be indexed

• They can have decimal values

• They must have integer values

What does a probability mass function (PMF) do?

• Assigns probabilities to continuous random variables

• Assigns probabilities to discrete random variables

• Calculates the mean of random variables

• Determines the variance of random variables

How is the probability of a discrete random variable represented?

• As a continuous function

• As a table or list

• As a pie chart

• As a histogram

What must the sum of all probabilities in a PMF equal?

• 0

• 1

• The number of possible outcomes

• The mean of the distribution

Which of the following is a property of a probability mass function?

• Probabilities must be non-negative

• Probabilities are always equal

• The sum of probabilities can exceed one

• Probabilities can be negative

What is a Bernoulli random variable?

• A variable that is always continuous

• A variable that can only take integer values

• A variable with more than two possible outcomes

• A variable with exactly two possible outcomes

In a Bernoulli random variable, what does the value '1' typically represent?

• Success

• Failure

• An error

• A neutral outcome

What is the probability of success in a Bernoulli trial if the probability of failure is 0.3?

• 0.7

• 1.0

• 0.5

• 0.3

Where is the Bernoulli random variable commonly used?

• In polynomial regression

• In logistic regression

• In time series analysis

• In linear regression