Probabilty

What is Bayes’ theorem?

• A) P(A∣B)=P(A∩B)P(A)P(A|B) = \frac{P(A \cap B)}{P(A)}P(A∣B)=P(A)P(A∩B)​
  

• B) P(A∣B)=P(B∣A)P(A)P(B)P(A|B) = \frac{P(B|A)P(A)}{P(B)}P(A∣B)=P(B)P(B∣A)P(A)​
  

• 
  C) P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B)P(A∩B)=P(A)P(B)
  

• 
  D) P(B∣A)=P(A∣B)P(B|A) = P(A|B)P(B∣A)=P(A∣B)

P(A ∩ B) for independent events A and B is...

• A) P(A)+P(B)P(A) + P(B)P(A)+P(B)
  

• B) P(A)P(B)P(A)P(B)P(A)P(B)
  

• 
  C) P(A∣B)P(A|B)P(A∣B)
  

• 
  D) P(A)/P(B)P(A)/P(B)P(A)/P(B)

The prior in Bayesian inference is defined as...

• A) Evidence from data
  

• 
  B) Updated belief after seeing data
  

• C) Initial belief before data
  

• 
  D) Marginal probability

The likelihood function in ML is...

• A) P(data)∗P(parameters)P(data)*P(parameters)P(data)∗P(parameters)
  

• P(parameters∣data)P(parameters|data)P(parameters∣data)
  

• C) P(data∣parameters)P(data|parameters)P(data∣parameters)
  

• 
  D) P(parameters)P(parameters)P(parameters)

Why use log-likelihood instead of raw likelihood?

• A) It’s always larger
  

• B) Avoids underflow and turns products into sums
  

• 
  C) To minimize variance
  

• 
  D) Simplifies denominators

A discrete random variable uses which function?

• A) PDF
  

• 
  B) CDF
  

• C) PMF (Probability Mass Function)
  

• 
  D) Joint PDF

For a continuous variable X, P(X=x)P(X = x)P(X=x) = ...

• A) f(x) (density)
  

• 
  B) > 0
  

• C)0
  

• 
  D) 1

Entropy measures...

• A) Average value
  

• 
  B) Spread or variance
  

• 
  C) Information content
  

• D) Uncertainty/randomness

Information gain in decision trees is based on...

• A) Variance
  

• 
  B) Entropy reduction
  

• 
  C) Mean
  

• 
  D) Likelihood ratio

Naive Bayes assumes features are...

• 10. A) Independent given the class
      

• 10. 
      B) Dependent across all classes
      

• 10. 
      C) Following normal distribution only
      

• 10. 
      D) Equal probabilities