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

The video tutorial covers Bernoulli trials, focusing on independent trials and their probability models. It introduces geometric random variables, explaining how they arise from independent Bernoulli trials. The tutorial also demonstrates how to construct a probability mass function (PMF) for geometric random variables, emphasizing the concept of independence in trials.

What is a Bernoulli trial similar to?

• A dice roll

• A coin toss

• A card draw

• A roulette spin

What does it mean for Bernoulli trials to be independent?

• The outcome of one trial affects the next

• The trials are conducted simultaneously

• The trials use different coins

• The outcome of one trial does not affect the next

In a geometric random variable experiment, when do you stop tossing the coin?

• After a fixed number of tosses

• When a tail appears

• When a head appears

• After two heads in a row

What does the random variable X represent in a geometric random variable?

• The number of tails

• The number of tosses until the first head

• The number of heads

• The number of successful trials

How is the probability of X=2 calculated in a geometric random variable?

• Probability of two tails in a row

• Probability of two heads in a row

• Probability of a head followed by a tail

• Probability of a tail followed by a head

What is the probability of X=1 in a geometric random variable?

• Probability of a tail

• Probability of a head

• Probability of two heads

• Probability of two tails

What is the significance of the normalization property in a geometric random variable?

• It ensures the sum of probabilities exceeds one

• It ensures the sum of probabilities is less than one

• It ensures the sum of probabilities equals one

• It ensures the sum of probabilities is zero