Probability Statistics - The Foundations of Machine Learning - Continuous Distributions with the Help of an Example

The video tutorial explores continuous random variables, highlighting the challenges of infinite precision in probability calculations. It introduces the concept of likelihood as an alternative to probability for continuous variables. The tutorial explains the properties of likelihood functions and their integration to derive probabilities over ranges. It covers uniform continuous distribution and delves into normal distribution, including the standard normal distribution, emphasizing their significance in real-world data analysis.

Why is it challenging to assign a probability to an exact value of a continuous random variable?

• Because continuous variables are discrete.

• Because probabilities are always zero.

• Because there are infinite possible values.

• Because continuous variables have finite precision.

What term is used to describe the likelihood of a continuous random variable falling within a specific range?

• Certainty

• Probability

• Possibility

• Chance

What is the relationship between likelihood and probability in continuous random variables?

• Likelihood is the same as probability.

• Likelihood, when integrated over a range, gives probability.

• Likelihood is unrelated to probability.

• Likelihood is the inverse of probability.

In a uniform continuous distribution, what is true about the likelihood of different values?

• Only one value has a likelihood.

• All values have different likelihoods.

• All values have the same likelihood.

• Likelihoods are not defined.

What is the shape of the graph for a normal distribution?

• A bell curve

• A square

• A straight line

• A zigzag pattern

What are the two parameters that define a normal distribution?

• Mean and variance

• Mean and standard deviation

• Range and interquartile range

• Median and mode

What is the mean of a standard normal distribution?

• 2

• 1

• 3

• 0

How do you transform a normal distribution to a standard normal distribution?

• By multiplying by the standard deviation

• By adding the mean

• By dividing by the mean

• By subtracting the mean and dividing by the standard deviation

What is the standard deviation of a standard normal distribution?

• 0

• 3

• 1

• 2

Why is the normal distribution important in statistics?

• It is not applicable to real-world data.

• It is only used in theoretical studies.

• It is the most commonly occurring distribution.

• It is rarely used.