A company wants to predict whether a customer will make a purchase based on their browsing history, time spent on the site, and past purchase behavior. Which type of learning would be most appropriate?

• Supervised Learning

• Semi Supevised Learning

• Reinforment Learning

• Unsupervised Learning

A weather forecasting team uses historical temperature data (time vs. temperature) and wants to model the relationship between time and temperature using a polynomial curve. What is the primary objective of using polynomial curve fitting in this context?

• To classify temperature data into categories

• To find the relationship between time and temperature

• To detect anomalies in temperature data

• To reduce the dimensionality of the data

What happens if a very high-degree polynomial is used for curve fitting?

• It leads to a better generalization on unseen data

• It ensures the model is simpler and less complex

• It may lead to overfitting, capturing noise rather than the underlying pattern

• It will always provide the best fit

What is the sum of the probabilities of all possible outcomes of a discrete random variable?

• 0

• 1

• Both 0 and 1

• Depends on the variable

• Can be greater than 1 if there are many outcomes

Bayes’ rule is used for which of the following purposes?

• To calculate the probability of the union of two events

• To find the probability of the intersection of two independent events

• To update the probability of a hypothesis given new evidence

• To determine if two events are mutually exclusive

Which of the following statements is correct regarding conditional probability?

• Conditional probability is the probability of an event occurring without any given conditions.

• It is always equal to the unconditional probability of the event.

• It only applies to continuous random variables.

• Conditional probability is used when the occurrence of one event affects the likelihood of another.

What is the probability of a continuous random variable taking any exact value?

• Always 1

• Always 0

• only 0 and 1

• Equal to the density at that value

• Depends on the value

The expected value (mean) of a continuous random variable X with probability density function f(x) is calculated using:

• ∫ f(x)dx

• ∫ x f(x)dx

• ∫ x dx

• ∫ x^2 f(x)dx

What does the quantile of a continuous random variable represent?

• The probability density at a given point

• The expected value of the random variable

• The sum of all possible values of the random variable

• A value below which a specified proportion of observations fall

The variance of a continuous random variable X is minimized when:

• All values of X are equal to the mean.

• X has a large spread around the mean.

• X takes only positive values.

• The variance is always zero.